This table of Grassmannian packings was created by N. J. A. Sloane based on joint work with R. H. Hardin and J. H. Conway in Packing lines, planes, etc.: packings in Grassmannian spaces (Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645). Sloane has since retired from AT&T Labs, and I’ve taken over maintaining the table. Please let me know if you can improve on any of these records.
See the paper for definitions and background. The squared chordal distance column lists the largest value known for any packing of N subspaces of dimension n in m dimensions, while the bound column lists the minimum of the simplex and orthoplex bounds from Section 5 of the paper and the trivial upper bound d2≤n. This upper bound is always rounded up, while the squared chordal distance is rounded down. Cases in which these bounds agree up to rounding are marked with ∗, and the notes column gives credit for improvements to the original table or further information, such as whether the listed upper bound is tight (i.e., whether there exists a code that exactly meets the bound).
You can download a tar file of all these configurations here. The file names are of the form m–n–N.txt, and the files list one vector per line, with m coordinates separated by commas. The first n lines specify an orthonormal basis for the first subspace, and so on.
Packings of N subspaces of dimension n in m dimensions
| m | n | N | Squared chordal distance | Bound | Notes |
|---|---|---|---|---|---|
| ∗ 3 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 3 | 1 | 4 | 0.8888888888 | 0.8888888889 | tight bound |
| 3 | 1 | 5 | 0.7999999999 | 0.8333333334 | |
| ∗ 3 | 1 | 6 | 0.7999999999 | 0.8000000000 | tight bound |
| ∗ 3 | 1 | 7 | 0.6666666666 | 0.6666666667 | tight bound |
| 3 | 1 | 8 | 0.5806285146 | 0.6666666667 | |
| 3 | 1 | 9 | 0.5519540855 | 0.6666666667 | |
| 3 | 1 | 10 | 0.5292109924 | 0.6666666667 | |
| 3 | 1 | 11 | 0.4895833489 | ||
| 3 | 1 | 12 | 0.4456887214 | ||
| 3 | 1 | 13 | 0.4099649711 | ||
| 3 | 1 | 14 | 0.3906289921 | ||
| 3 | 1 | 15 | 0.3813256141 | ||
| 3 | 1 | 16 | 0.3685242696 | ||
| 3 | 1 | 17 | 0.3328546988 | ||
| 3 | 1 | 18 | 0.3193305211 | ||
| 3 | 1 | 19 | 0.3000093877 | ||
| 3 | 1 | 20 | 0.2919740686 | Henry Cohn, 2023 | |
| 3 | 1 | 21 | 0.2842099468 | ||
| 3 | 1 | 22 | 0.2793283319 | Henry Cohn, 2023 | |
| 3 | 1 | 23 | 0.2576904035 | ||
| 3 | 1 | 24 | 0.2524640360 | ||
| 3 | 1 | 25 | 0.2387298379 | ||
| 3 | 1 | 26 | 0.2308008695 | Henry Cohn, 2024 | |
| 3 | 1 | 27 | 0.2240235782 | ||
| 3 | 1 | 28 | 0.2181978117 | ||
| 3 | 1 | 29 | 0.2135612070 | Henry Cohn, 2023 | |
| 3 | 1 | 30 | 0.2060838295 | ||
| 3 | 1 | 31 | 0.1990747916 | Henry Cohn, 2023 | |
| 3 | 1 | 32 | 0.1914782380 | ||
| 3 | 1 | 33 | 0.1863557638 | ||
| 3 | 1 | 34 | 0.1820514756 | ||
| 3 | 1 | 35 | 0.1768735418 | ||
| 3 | 1 | 36 | 0.1729747303 | Henry Cohn, 2023 | |
| 3 | 1 | 37 | 0.1691598522 | Henry Cohn, 2024 | |
| 3 | 1 | 38 | 0.1665869354 | Henry Cohn, 2024 | |
| 3 | 1 | 39 | 0.1634073776 | ||
| 3 | 1 | 40 | 0.1568275595 | ||
| 3 | 1 | 41 | 0.1525644706 | ||
| 3 | 1 | 42 | 0.1490203035 | Henry Cohn, 2023 | |
| 3 | 1 | 43 | 0.1469199238 | Henry Cohn, 2025 | |
| 3 | 1 | 44 | 0.1427787500 | ||
| 3 | 1 | 45 | 0.1409157797 | Henry Cohn, 2024 | |
| 3 | 1 | 46 | 0.1384267791 | ||
| 3 | 1 | 47 | 0.1362449197 | Henry Cohn, 2025 | |
| 3 | 1 | 48 | 0.1339227101 | ||
| 3 | 1 | 49 | 0.1303178440 | Henry Cohn, 2023 | |
| 3 | 1 | 50 | 0.1271717953 | ||
| 3 | 1 | 51 | 0.1248341142 | Henry Cohn, 2025 | |
| 3 | 1 | 52 | 0.1225478939 | Henry Cohn, 2025 | |
| 3 | 1 | 53 | 0.1200068656 | ||
| 3 | 1 | 54 | 0.1187276434 | ||
| 3 | 1 | 55 | 0.1182184210 | Henry Cohn, 2025 | |
| 3 | 1 | 56 | 0.1153881344 | ||
| 3 | 1 | 57 | 0.1130094390 | Henry Cohn, 2024 | |
| 3 | 1 | 58 | 0.1112963897 | ||
| 3 | 1 | 59 | 0.1094202828 | ||
| 3 | 1 | 60 | 0.1079786078 | ||
| 3 | 1 | 61 | 0.1058337052 | ||
| 3 | 1 | 62 | 0.1040628389 | ||
| 3 | 1 | 63 | 0.1026596852 | Henry Cohn, 2024 | |
| 3 | 1 | 64 | 0.1007631182 | ||
| 3 | 1 | 65 | 0.0995552862 | Henry Cohn, 2024 | |
| 3 | 1 | 66 | 0.0988730140 | ||
| 3 | 1 | 67 | 0.0973798467 | ||
| 3 | 1 | 68 | 0.0957307154 | ||
| 3 | 1 | 69 | 0.0944620424 | Henry Cohn, 2024 | |
| 3 | 1 | 70 | 0.0931842175 | Henry Cohn, 2025 | |
| 3 | 1 | 71 | 0.0923400457 | Henry Cohn, 2025 | |
| 3 | 1 | 72 | 0.0907725757 | Henry Cohn, 2024 | |
| 3 | 1 | 73 | 0.0894325531 | ||
| 3 | 1 | 74 | 0.0881099899 | Henry Cohn, 2025 | |
| 3 | 1 | 75 | 0.0873637664 | Henry Cohn, 2024 | |
| 3 | 1 | 76 | 0.0858021401 | Henry Cohn, 2024 | |
| 3 | 1 | 77 | 0.0847837362 | Henry Cohn, 2024 | |
| 3 | 1 | 78 | 0.0838816516 | Henry Cohn, 2024 | |
| 3 | 1 | 79 | 0.0829424657 | Henry Cohn, 2024 | |
| 3 | 1 | 80 | 0.0820619908 | Henry Cohn, 2024 | |
| 3 | 1 | 81 | 0.0816197151 | ||
| 3 | 1 | 82 | 0.0800907073 | Henry Cohn, 2024 | |
| 3 | 1 | 83 | 0.0791280951 | Henry Cohn, 2025 | |
| 3 | 1 | 84 | 0.0782592507 | Henry Cohn, 2025 | |
| 3 | 1 | 85 | 0.0772151335 | Henry Cohn, 2024 | |
| 3 | 1 | 86 | 0.0762818491 | Henry Cohn, 2024 | |
| 3 | 1 | 87 | 0.0753880851 | Henry Cohn, 2024 | |
| 3 | 1 | 88 | 0.0745983218 | Henry Cohn, 2025 | |
| 3 | 1 | 89 | 0.0737475124 | Henry Cohn, 2024 | |
| 3 | 1 | 90 | 0.0729197231 | Henry Cohn, 2024 | |
| 3 | 1 | 91 | 0.0721306421 | Henry Cohn, 2024 | |
| 3 | 1 | 92 | 0.0714686162 | Henry Cohn, 2024 | |
| 3 | 1 | 93 | 0.0708630841 | Henry Cohn, 2024 | |
| 3 | 1 | 94 | 0.0705147106 | Henry Cohn, 2024 | |
| 3 | 1 | 95 | 0.0697193685 | Henry Cohn, 2025 | |
| 3 | 1 | 96 | 0.0693820018 | Henry Cohn, 2024 | |
| 3 | 1 | 97 | 0.0683016779 | Henry Cohn, 2024 | |
| 3 | 1 | 98 | 0.0675501458 | Henry Cohn, 2025 | |
| 3 | 1 | 99 | 0.0668607357 | ||
| 3 | 1 | 100 | 0.0660334922 | Henry Cohn, 2024 | |
| ∗ 4 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 4 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 4 | 1 | 5 | 0.9374999999 | 0.9375000000 | tight bound |
| 4 | 1 | 6 | 0.8888888888 | 0.9000000000 | |
| 4 | 1 | 7 | 0.8475970508 | 0.8750000000 | |
| 4 | 1 | 8 | 0.8284271247 | 0.8571428572 | |
| 4 | 1 | 9 | 0.8114195153 | 0.8437500000 | |
| 4 | 1 | 10 | 0.8114195153 | 0.8333333334 | |
| ∗ 4 | 1 | 11 | 0.7499999999 | 0.7500000000 | tight bound |
| ∗ 4 | 1 | 12 | 0.7499999999 | 0.7500000000 | tight bound |
| 4 | 1 | 13 | 0.6786070758 | 0.7500000000 | |
| 4 | 1 | 14 | 0.6518097061 | 0.7500000000 | |
| 4 | 1 | 15 | 0.6294363286 | 0.7500000000 | |
| 4 | 1 | 16 | 0.6180339887 | 0.7500000000 | |
| 4 | 1 | 17 | 0.6020261183 | 0.7500000000 | |
| 4 | 1 | 18 | 0.5946802049 | 0.7500000000 | |
| 4 | 1 | 19 | 0.5818451952 | ||
| 4 | 1 | 20 | 0.5736095486 | ||
| 4 | 1 | 21 | 0.5617658936 | Henry Cohn, 2023 | |
| 4 | 1 | 22 | 0.5480896962 | ||
| 4 | 1 | 23 | 0.5263485431 | ||
| 4 | 1 | 24 | 0.5182842211 | ||
| 4 | 1 | 25 | 0.4990787241 | Henry Cohn, 2024 | |
| 4 | 1 | 26 | 0.4887185391 | ||
| 4 | 1 | 27 | 0.4747566702 | ||
| 4 | 1 | 28 | 0.4678482018 | ||
| 4 | 1 | 29 | 0.4593349488 | ||
| 4 | 1 | 30 | 0.4523404552 | Henry Cohn, 2024 | |
| 4 | 1 | 31 | 0.4480651540 | Henry Cohn, 2024 | |
| 4 | 1 | 32 | 0.4469610677 | ||
| 4 | 1 | 33 | 0.4383367891 | Henry Cohn, 2025 | |
| 4 | 1 | 34 | 0.4294553058 | Henry Cohn, 2023 | |
| 4 | 1 | 35 | 0.4258134468 | Henry Cohn, 2024 | |
| 4 | 1 | 36 | 0.4240825190 | Henry Cohn, 2023 | |
| 4 | 1 | 37 | 0.4208973371 | ||
| 4 | 1 | 38 | 0.4207805760 | ||
| 4 | 1 | 39 | 0.4076830992 | Henry Cohn, 2024 | |
| 4 | 1 | 40 | 0.3964466094 | ||
| 4 | 1 | 41 | 0.3881129259 | Henry Cohn, 2024 | |
| 4 | 1 | 42 | 0.3842853799 | ||
| 4 | 1 | 43 | 0.3753741606 | Henry Cohn, 2024 | |
| 4 | 1 | 44 | 0.3680303751 | Henry Cohn, 2024 | |
| 4 | 1 | 45 | 0.3641925285 | ||
| 4 | 1 | 46 | 0.3621764445 | ||
| 4 | 1 | 47 | 0.3555499094 | Henry Cohn, 2025 | |
| 4 | 1 | 48 | 0.3514548200 | Henry Cohn, 2025 | |
| 4 | 1 | 49 | 0.3477892791 | Henry Cohn, 2023 | |
| 4 | 1 | 50 | 0.3468281123 | Henry Cohn, 2023 | |
| 4 | 1 | 51 | 0.3456505782 | Henry Cohn, 2025 | |
| 4 | 1 | 52 | 0.3455125356 | Henry Cohn, 2025 | |
| 4 | 1 | 53 | 0.3454915192 | Henry Cohn, 2025 | |
| 4 | 1 | 54 | 0.3454915028 | ||
| 4 | 1 | 55 | 0.3454915028 | ||
| 4 | 1 | 56 | 0.3454915028 | ||
| 4 | 1 | 57 | 0.3454915028 | ||
| 4 | 1 | 58 | 0.3454915028 | ||
| 4 | 1 | 59 | 0.3454915028 | ||
| 4 | 1 | 60 | 0.3454915028 | ||
| 4 | 1 | 61 | 0.3105454289 | Henry Cohn, 2025 | |
| 4 | 1 | 62 | 0.3078403016 | Henry Cohn, 2024 | |
| 4 | 1 | 63 | 0.3057061005 | Henry Cohn, 2025 | |
| 4 | 1 | 64 | 0.3011051204 | Henry Cohn, 2024 | |
| 4 | 1 | 65 | 0.2981420632 | Henry Cohn, 2025 | |
| 4 | 1 | 66 | 0.2952448218 | Henry Cohn, 2025 | |
| 4 | 1 | 67 | 0.2924845812 | Henry Cohn, 2024 | |
| 4 | 1 | 68 | 0.2896638866 | Henry Cohn, 2024 | |
| 4 | 1 | 69 | 0.2867158162 | Henry Cohn, 2024 | |
| 4 | 1 | 70 | 0.2843020279 | Henry Cohn, 2024 | |
| 4 | 1 | 71 | 0.2808398454 | Henry Cohn, 2025 | |
| 4 | 1 | 72 | 0.2780138931 | Henry Cohn, 2024 | |
| 4 | 1 | 73 | 0.2757190113 | Henry Cohn, 2024 | |
| 4 | 1 | 74 | 0.2731426475 | Henry Cohn, 2024 | |
| 4 | 1 | 75 | 0.2711333377 | ||
| 4 | 1 | 76 | 0.2705772291 | ||
| 4 | 1 | 77 | 0.2669677977 | Henry Cohn, 2025 | |
| 4 | 1 | 78 | 0.2652983970 | Henry Cohn, 2025 | |
| 4 | 1 | 79 | 0.2634487978 | Henry Cohn, 2025 | |
| 4 | 1 | 80 | 0.2622051439 | ||
| 4 | 1 | 81 | 0.2605350596 | Henry Cohn, 2025 | |
| 4 | 1 | 82 | 0.2590078935 | Henry Cohn, 2024 | |
| 4 | 1 | 83 | 0.2580022875 | ||
| 4 | 1 | 84 | 0.2569464254 | ||
| 4 | 1 | 85 | 0.2559903260 | Henry Cohn, 2024 | |
| 4 | 1 | 86 | 0.2541576422 | ||
| 4 | 1 | 87 | 0.2531183733 | ||
| 4 | 1 | 88 | 0.2517548171 | ||
| 4 | 1 | 89 | 0.2500341112 | ||
| 4 | 1 | 90 | 0.2489408103 | ||
| 4 | 1 | 91 | 0.2478752232 | Henry Cohn, 2025 | |
| 4 | 1 | 92 | 0.2462380417 | ||
| 4 | 1 | 93 | 0.2431222205 | ||
| 4 | 1 | 94 | 0.2415782915 | ||
| 4 | 1 | 95 | 0.2410949781 | ||
| 4 | 1 | 96 | 0.2402333903 | Henry Cohn, 2024 | |
| 4 | 1 | 97 | 0.2396265587 | ||
| 4 | 1 | 98 | 0.2360782975 | ||
| 4 | 1 | 99 | 0.2330137509 | Henry Cohn, 2024 | |
| 4 | 1 | 100 | 0.2313643538 | ||
| ∗ 4 | 2 | 3 | 1.4999999999 | 1.5000000000 | tight bound [5] |
| ∗ 4 | 2 | 4 | 1.3333333333 | 1.3333333334 | tight bound [5] |
| ∗ 4 | 2 | 5 | 1.2499999999 | 1.2500000000 | tight bound [5] |
| ∗ 4 | 2 | 6 | 1.1999999999 | 1.2000000000 | tight bound [5] |
| ∗ 4 | 2 | 7 | 1.1666666666 | 1.1666666667 | tight bound [4] |
| ∗ 4 | 2 | 8 | 1.1428571428 | 1.1428571429 | tight bound [4] |
| 4 | 2 | 9 | 1.1230624449 | 1.1250000000 | |
| ∗ 4 | 2 | 10 | 1.1111111111 | 1.1111111112 | tight bound [5] |
| ∗ 4 | 2 | 11 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 12 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 13 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 14 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 15 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 16 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 17 | 0.9999999999 | 1.0000000000 | tight bound [5] |
| ∗ 4 | 2 | 18 | 1.0000000000 | 1.0000000000 | tight bound [5] |
| 4 | 2 | 19 | 0.9090909090 | ||
| 4 | 2 | 20 | 0.9090909090 | ||
| 4 | 2 | 21 | 0.8683658001 | ||
| 4 | 2 | 22 | 0.8628666150 | ||
| 4 | 2 | 23 | 0.8450645945 | ||
| 4 | 2 | 24 | 0.8371591062 | ||
| 4 | 2 | 25 | 0.8275329668 | ||
| 4 | 2 | 26 | 0.8143605100 | ||
| 4 | 2 | 27 | 0.8056026757 | ||
| 4 | 2 | 28 | 0.8004820811 | ||
| 4 | 2 | 29 | 0.7888843622 | ||
| 4 | 2 | 30 | 0.7809079178 | ||
| 4 | 2 | 31 | 0.7760213858 | ||
| 4 | 2 | 32 | 0.7690588539 | ||
| 4 | 2 | 33 | 0.7591707968 | ||
| 4 | 2 | 34 | 0.7548790292 | ||
| 4 | 2 | 35 | 0.7489100760 | ||
| 4 | 2 | 36 | 0.7476820831 | ||
| 4 | 2 | 37 | 0.7286336898 | ||
| 4 | 2 | 38 | 0.7197930166 | ||
| 4 | 2 | 39 | 0.7095125538 | ||
| 4 | 2 | 40 | 0.7066332130 | ||
| 4 | 2 | 41 | 0.6991501607 | ||
| 4 | 2 | 42 | 0.6948392861 | ||
| 4 | 2 | 43 | 0.6873492339 | ||
| 4 | 2 | 44 | 0.6830542529 | ||
| 4 | 2 | 45 | 0.6809212206 | ||
| 4 | 2 | 46 | 0.6793062616 | ||
| 4 | 2 | 47 | 0.6732073544 | ||
| 4 | 2 | 48 | 0.6666666666 | ||
| 4 | 2 | 49 | 0.6666666666 | ||
| 4 | 2 | 50 | 0.6666666666 | ||
| 4 | 2 | 51 | 0.6451736243 | ||
| 4 | 2 | 52 | 0.6418388415 | ||
| 4 | 2 | 53 | 0.6386335039 | ||
| 4 | 2 | 54 | 0.6352433706 | ||
| 4 | 2 | 55 | 0.6261328087 | ||
| 4 | 2 | 56 | 0.6209010269 | ||
| 4 | 2 | 57 | 0.6165526639 | ||
| 4 | 2 | 58 | 0.6117237441 | ||
| 4 | 2 | 59 | 0.6068425752 | ||
| 4 | 2 | 60 | 0.6034819166 | ||
| 4 | 2 | 61 | 0.5965096744 | ||
| 4 | 2 | 62 | 0.5940066796 | ||
| 4 | 2 | 63 | 0.5914380371 | ||
| 4 | 2 | 64 | 0.5886499936 | ||
| 4 | 2 | 65 | 0.5874799268 | ||
| 4 | 2 | 66 | 0.5861433262 | ||
| 4 | 2 | 67 | 0.5813543366 | ||
| 4 | 2 | 68 | 0.5747791689 | ||
| 4 | 2 | 69 | 0.5724737529 | ||
| 4 | 2 | 70 | 0.5711761177 | ||
| 4 | 2 | 71 | 0.5701324984 | ||
| 4 | 2 | 72 | 0.5693277415 | ||
| 4 | 2 | 73 | 0.5568283864 | ||
| 4 | 2 | 74 | 0.5519878460 | ||
| 4 | 2 | 75 | 0.5482525630 | ||
| 4 | 2 | 76 | 0.5455746922 | ||
| 4 | 2 | 77 | 0.5371513899 | ||
| 4 | 2 | 78 | 0.5351790868 | ||
| 4 | 2 | 79 | 0.5313580520 | ||
| 4 | 2 | 80 | 0.5283330696 | ||
| 4 | 2 | 81 | 0.5253256670 | ||
| 4 | 2 | 82 | 0.5229513551 | ||
| 4 | 2 | 83 | 0.5205961394 | ||
| 4 | 2 | 84 | 0.5202100447 | ||
| 4 | 2 | 85 | 0.5180517909 | ||
| 4 | 2 | 86 | 0.5151194839 | ||
| 4 | 2 | 87 | 0.5142077874 | ||
| 4 | 2 | 88 | 0.5140751665 | ||
| 4 | 2 | 89 | 0.5138966061 | ||
| 4 | 2 | 90 | 0.5135005785 | ||
| 4 | 2 | 91 | 0.5091747480 | ||
| 4 | 2 | 92 | 0.5082491411 | ||
| 4 | 2 | 93 | 0.5071006338 | ||
| 4 | 2 | 94 | 0.5060761145 | ||
| 4 | 2 | 95 | 0.5041046164 | ||
| 4 | 2 | 96 | 0.5022838770 | ||
| 4 | 2 | 97 | 0.5017034805 | ||
| 4 | 2 | 98 | 0.5015831202 | ||
| 4 | 2 | 99 | 0.5010215202 | ||
| 4 | 2 | 100 | 0.5008698794 | ||
| ∗ 5 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 5 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 5 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 5 | 1 | 6 | 0.9599999999 | 0.9600000000 | tight bound |
| 5 | 1 | 7 | 0.9180848294 | 0.9333333334 | |
| 5 | 1 | 8 | 0.8918889086 | 0.9142857143 | |
| 5 | 1 | 9 | 0.8888888888 | 0.9000000000 | |
| ∗ 5 | 1 | 10 | 0.8888888888 | 0.8888888889 | tight bound |
| 5 | 1 | 11 | 0.8505085833 | 0.8800000000 | |
| 5 | 1 | 12 | 0.8475970508 | 0.8727272728 | |
| 5 | 1 | 13 | 0.8310735125 | 0.8666666667 | |
| 5 | 1 | 14 | 0.8309716701 | 0.8615384616 | |
| 5 | 1 | 15 | 0.8284271247 | 0.8571428572 | |
| ∗ 5 | 1 | 16 | 0.7999999999 | 0.8000000000 | tight bound |
| 5 | 1 | 17 | 0.7687312456 | 0.8000000000 | Henry Cohn, 2025 |
| 5 | 1 | 18 | 0.7657449677 | 0.8000000000 | |
| 5 | 1 | 19 | 0.7499999999 | 0.8000000000 | |
| 5 | 1 | 20 | 0.7499999999 | 0.8000000000 | |
| 5 | 1 | 21 | 0.7065913748 | 0.8000000000 | |
| 5 | 1 | 22 | 0.6930459625 | 0.8000000000 | |
| 5 | 1 | 23 | 0.6806468838 | 0.8000000000 | Henry Cohn, 2025 |
| 5 | 1 | 24 | 0.6747429559 | 0.8000000000 | |
| 5 | 1 | 25 | 0.6691901151 | 0.8000000000 | |
| 5 | 1 | 26 | 0.6580191687 | 0.8000000000 | Henry Cohn, 2025 |
| 5 | 1 | 27 | 0.6468567046 | 0.8000000000 | |
| 5 | 1 | 28 | 0.6421785148 | 0.8000000000 | |
| 5 | 1 | 29 | 0.6381208631 | Henry Cohn, 2024 | |
| 5 | 1 | 30 | 0.6341439740 | Henry Cohn, 2025 | |
| 5 | 1 | 31 | 0.6279257366 | ||
| 5 | 1 | 32 | 0.6266920713 | ||
| 5 | 1 | 33 | 0.6251305099 | ||
| 5 | 1 | 34 | 0.6184811046 | ||
| 5 | 1 | 35 | 0.6180339887 | ||
| 5 | 1 | 36 | 0.6180339887 | ||
| 5 | 1 | 37 | 0.6180339887 | ||
| 5 | 1 | 38 | 0.5931996071 | Henry Cohn, 2023 | |
| 5 | 1 | 39 | 0.5878738637 | Henry Cohn, 2024 | |
| 5 | 1 | 40 | 0.5799099406 | Henry Cohn, 2023 | |
| 5 | 1 | 41 | 0.5740768631 | ||
| 5 | 1 | 42 | 0.5643156569 | Henry Cohn, 2023 | |
| 5 | 1 | 43 | 0.5592551525 | Henry Cohn, 2024 | |
| 5 | 1 | 44 | 0.5539224156 | ||
| 5 | 1 | 45 | 0.5483442914 | Henry Cohn, 2023 | |
| 5 | 1 | 46 | 0.5414095503 | ||
| 5 | 1 | 47 | 0.5354411857 | Henry Cohn, 2024 | |
| 5 | 1 | 48 | 0.5298355630 | Henry Cohn, 2024 | |
| 5 | 1 | 49 | 0.5250335140 | Henry Cohn, 2024 | |
| 5 | 1 | 50 | 0.5202588767 | Henry Cohn, 2024 | |
| 5 | 1 | 51 | 0.5142269208 | Henry Cohn, 2024 | |
| 5 | 1 | 52 | 0.5102676921 | Henry Cohn, 2024 | |
| 5 | 1 | 53 | 0.5068372749 | Henry Cohn, 2025 | |
| 5 | 1 | 54 | 0.5034930736 | Henry Cohn, 2024 | |
| 5 | 1 | 55 | 0.4996299524 | Henry Cohn, 2025 | |
| 5 | 1 | 56 | 0.4978085353 | Henry Cohn, 2025 | |
| 5 | 1 | 57 | 0.4956421213 | Henry Cohn, 2024 | |
| 5 | 1 | 58 | 0.4919358685 | ||
| 5 | 1 | 59 | 0.4895549039 | Henry Cohn, 2024 | |
| 5 | 1 | 60 | 0.4875241920 | Henry Cohn, 2025 | |
| 5 | 1 | 61 | 0.4863699814 | Henry Cohn, 2025 | |
| 5 | 1 | 62 | 0.4812907936 | Henry Cohn, 2024 | |
| 5 | 1 | 63 | 0.4786081822 | Henry Cohn, 2024 | |
| 5 | 1 | 64 | 0.4756326343 | Henry Cohn, 2024 | |
| 5 | 1 | 65 | 0.4734766842 | Henry Cohn, 2024 | |
| 5 | 1 | 66 | 0.4706429650 | Henry Cohn, 2024 | |
| 5 | 1 | 67 | 0.4683085185 | ||
| 5 | 1 | 68 | 0.4660710287 | Henry Cohn, 2024 | |
| 5 | 1 | 69 | 0.4643123376 | Henry Cohn, 2024 | |
| 5 | 1 | 70 | 0.4628418084 | Henry Cohn, 2024 | |
| 5 | 1 | 71 | 0.4607714717 | Henry Cohn, 2024 | |
| 5 | 1 | 72 | 0.4588928486 | Henry Cohn, 2024 | |
| 5 | 1 | 73 | 0.4571630770 | Henry Cohn, 2024 | |
| 5 | 1 | 74 | 0.4561092407 | ||
| 5 | 1 | 75 | 0.4548400944 | Henry Cohn, 2024 | |
| 5 | 1 | 76 | 0.4525512368 | Henry Cohn, 2024 | |
| 5 | 1 | 77 | 0.4492901527 | ||
| 5 | 1 | 78 | 0.4463644226 | ||
| 5 | 1 | 79 | 0.4448778309 | ||
| 5 | 1 | 80 | 0.4416523625 | ||
| 5 | 1 | 81 | 0.4383415948 | Henry Cohn, 2024 | |
| 5 | 1 | 82 | 0.4356162671 | ||
| 5 | 1 | 83 | 0.4336216395 | ||
| 5 | 1 | 84 | 0.4310365993 | ||
| 5 | 1 | 85 | 0.4284713947 | Henry Cohn, 2024 | |
| 5 | 1 | 86 | 0.4263419158 | ||
| 5 | 1 | 87 | 0.4228189406 | ||
| 5 | 1 | 88 | 0.4204097656 | ||
| 5 | 1 | 89 | 0.4172422362 | ||
| 5 | 1 | 90 | 0.4148622928 | ||
| 5 | 1 | 91 | 0.4125488092 | ||
| 5 | 1 | 92 | 0.4099314220 | ||
| 5 | 1 | 93 | 0.4070101986 | ||
| 5 | 1 | 94 | 0.4047564145 | ||
| 5 | 1 | 95 | 0.4021847400 | ||
| 5 | 1 | 96 | 0.3999875102 | ||
| 5 | 1 | 97 | 0.3977256548 | ||
| 5 | 1 | 98 | 0.3957004779 | ||
| 5 | 1 | 99 | 0.3937862470 | ||
| 5 | 1 | 100 | 0.3918423693 | ||
| 5 | 2 | 3 | 1.7499999999 | 1.8000000000 | |
| ∗ 5 | 2 | 4 | 1.5999999999 | 1.6000000000 | tight bound [4] |
| ∗ 5 | 2 | 5 | 1.4999999999 | 1.5000000000 | tight bound [4] |
| ∗ 5 | 2 | 6 | 1.4399999999 | 1.4400000000 | tight bound [4] |
| ∗ 5 | 2 | 7 | 1.3999999999 | 1.4000000000 | tight bound [4] |
| ∗ 5 | 2 | 8 | 1.3714285714 | 1.3714285715 | tight bound [4] |
| ∗ 5 | 2 | 9 | 1.3499999999 | 1.3500000000 | tight bound [4] |
| ∗ 5 | 2 | 10 | 1.3333333333 | 1.3333333334 | tight bound [4] |
| ∗ 5 | 2 | 11 | 1.3199999999 | 1.3200000000 | tight bound [4] |
| 5 | 2 | 12 | 1.3063520860 | 1.3090909091 | |
| 5 | 2 | 13 | 1.2941906871 | 1.3000000000 | |
| 5 | 2 | 14 | 1.2790114729 | 1.2923076924 | |
| 5 | 2 | 15 | 1.2707462652 | 1.2857142858 | |
| ∗ 5 | 2 | 16 | 1.1999999999 | 1.2000000000 | |
| ∗ 5 | 2 | 17 | 1.1999999999 | 1.2000000000 | |
| 5 | 2 | 18 | 1.1908530119 | 1.2000000000 | |
| 5 | 2 | 19 | 1.1761278309 | 1.2000000000 | |
| 5 | 2 | 20 | 1.1619417514 | 1.2000000000 | |
| 5 | 2 | 21 | 1.1542745973 | 1.2000000000 | |
| 5 | 2 | 22 | 1.1419030833 | 1.2000000000 | |
| 5 | 2 | 23 | 1.1332177715 | 1.2000000000 | |
| 5 | 2 | 24 | 1.1251403012 | 1.2000000000 | |
| 5 | 2 | 25 | 1.1178106155 | 1.2000000000 | |
| 5 | 2 | 26 | 1.1113470553 | 1.2000000000 | |
| 5 | 2 | 27 | 1.1044758153 | 1.2000000000 | |
| 5 | 2 | 28 | 1.0989455424 | 1.2000000000 | |
| 5 | 2 | 29 | 1.0936717022 | ||
| 5 | 2 | 30 | 1.0874780286 | ||
| 5 | 2 | 31 | 1.0828576060 | ||
| 5 | 2 | 32 | 1.0768083597 | ||
| 5 | 2 | 33 | 1.0722129865 | ||
| 5 | 2 | 34 | 1.0671267695 | ||
| 5 | 2 | 35 | 1.0640453885 | ||
| 5 | 2 | 36 | 1.0595901891 | ||
| 5 | 2 | 37 | 1.0530112658 | ||
| 5 | 2 | 38 | 1.0462170817 | ||
| 5 | 2 | 39 | 1.0404669576 | ||
| 5 | 2 | 40 | 1.0354930698 | ||
| 5 | 2 | 41 | 1.0302008769 | ||
| 5 | 2 | 42 | 1.0256304636 | ||
| 5 | 2 | 43 | 1.0206811105 | ||
| 5 | 2 | 44 | 1.0160232501 | ||
| 5 | 2 | 45 | 1.0123028605 | ||
| 5 | 2 | 46 | 1.0083490289 | ||
| 5 | 2 | 47 | 1.0041839980 | ||
| 5 | 2 | 48 | 1.0004897361 | ||
| 5 | 2 | 49 | 0.9960708015 | ||
| 5 | 2 | 50 | 0.9909795337 | ||
| 5 | 2 | 51 | 0.9859553022 | ||
| 5 | 2 | 52 | 0.9793165685 | ||
| 5 | 2 | 53 | 0.9744234857 | ||
| 5 | 2 | 54 | 0.9691842943 | ||
| 5 | 2 | 55 | 0.9640070895 | ||
| 5 | 2 | 56 | 0.9595523020 | ||
| 5 | 2 | 57 | 0.9552049081 | ||
| 5 | 2 | 58 | 0.9508182269 | ||
| 5 | 2 | 59 | 0.9476497246 | ||
| 5 | 2 | 60 | 0.9433464971 | ||
| 5 | 2 | 61 | 0.9395372634 | ||
| 5 | 2 | 62 | 0.9358126747 | ||
| 5 | 2 | 63 | 0.9325153597 | ||
| 5 | 2 | 64 | 0.9299448338 | ||
| 5 | 2 | 65 | 0.9270049360 | ||
| 5 | 2 | 66 | 0.9242488409 | ||
| 5 | 2 | 67 | 0.9207887560 | ||
| 5 | 2 | 68 | 0.9183969493 | ||
| 5 | 2 | 69 | 0.9159690207 | ||
| 5 | 2 | 70 | 0.9129655235 | ||
| 5 | 2 | 71 | 0.9106042409 | ||
| 5 | 2 | 72 | 0.9085215953 | ||
| 5 | 2 | 73 | 0.9062459577 | ||
| 5 | 2 | 74 | 0.9044783404 | ||
| 5 | 2 | 75 | 0.9019207505 | ||
| 5 | 2 | 76 | 0.9002160140 | ||
| 5 | 2 | 77 | 0.8978108956 | ||
| 5 | 2 | 78 | 0.8952756903 | ||
| 5 | 2 | 79 | 0.8928232175 | ||
| 5 | 2 | 80 | 0.8905750842 | ||
| 5 | 2 | 81 | 0.8885532618 | ||
| 5 | 2 | 82 | 0.8861275165 | ||
| 5 | 2 | 83 | 0.8838574577 | ||
| 5 | 2 | 84 | 0.8817189815 | ||
| 5 | 2 | 85 | 0.8794881243 | ||
| 5 | 2 | 86 | 0.8773447972 | ||
| 5 | 2 | 87 | 0.8749526086 | ||
| 5 | 2 | 88 | 0.8729021574 | ||
| 5 | 2 | 89 | 0.8705823658 | ||
| 5 | 2 | 90 | 0.8683411832 | ||
| 5 | 2 | 91 | 0.8659446234 | ||
| 5 | 2 | 92 | 0.8639959068 | ||
| 5 | 2 | 93 | 0.8615902565 | ||
| 5 | 2 | 94 | 0.8590307301 | ||
| 5 | 2 | 95 | 0.8569011419 | ||
| 5 | 2 | 96 | 0.8546291110 | ||
| 5 | 2 | 97 | 0.8523999461 | ||
| 5 | 2 | 98 | 0.8500886646 | ||
| 5 | 2 | 99 | 0.8481295242 | ||
| 5 | 2 | 100 | 0.8458789916 | ||
| ∗ 6 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 6 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 6 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 6 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 6 | 1 | 7 | 0.9722222222 | 0.9722222223 | tight bound |
| 6 | 1 | 8 | 0.9419464180 | 0.9523809524 | |
| 6 | 1 | 9 | 0.9225724578 | 0.9375000000 | |
| 6 | 1 | 10 | 0.9211646096 | 0.9259259260 | |
| 6 | 1 | 11 | 0.8999999999 | 0.9166666667 | |
| 6 | 1 | 12 | 0.8999999999 | 0.9090909091 | |
| 6 | 1 | 13 | 0.8888888888 | 0.9027777778 | |
| 6 | 1 | 14 | 0.8888888888 | 0.8974358975 | |
| 6 | 1 | 15 | 0.8888888888 | 0.8928571429 | |
| ∗ 6 | 1 | 16 | 0.8888888888 | 0.8888888889 | tight bound |
| 6 | 1 | 17 | 0.8610152062 | 0.8854166667 | Henry Cohn, 2023 |
| 6 | 1 | 18 | 0.8524029546 | 0.8823529412 | Henry Cohn, 2023 |
| 6 | 1 | 19 | 0.8519454666 | 0.8796296297 | |
| 6 | 1 | 20 | 0.8485780899 | 0.8771929825 | |
| 6 | 1 | 21 | 0.8475970508 | 0.8750000000 | |
| ∗ 6 | 1 | 22 | 0.8333333333 | 0.8333333334 | tight bound |
| 6 | 1 | 23 | 0.8033322387 | 0.8333333334 | Henry Cohn, 2024 |
| 6 | 1 | 24 | 0.8024691358 | 0.8333333334 | |
| 6 | 1 | 25 | 0.7857005372 | 0.8333333334 | |
| 6 | 1 | 26 | 0.7757930287 | 0.8333333334 | Henry Cohn, 2024 |
| 6 | 1 | 27 | 0.7709404199 | 0.8333333334 | Henry Cohn, 2025 |
| 6 | 1 | 28 | 0.7581504237 | 0.8333333334 | Henry Cohn, 2023 |
| 6 | 1 | 29 | 0.7520323607 | 0.8333333334 | Henry Cohn, 2025 |
| 6 | 1 | 30 | 0.7505950831 | 0.8333333334 | Henry Cohn, 2025 |
| 6 | 1 | 31 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 32 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 33 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 34 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 35 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 36 | 0.7499999999 | 0.8333333334 | |
| 6 | 1 | 37 | 0.7150548581 | 0.8333333334 | Henry Cohn, 2023 |
| 6 | 1 | 38 | 0.7050520410 | 0.8333333334 | |
| 6 | 1 | 39 | 0.7007459519 | 0.8333333334 | Henry Cohn, 2025 |
| 6 | 1 | 40 | 0.6881048262 | 0.8333333334 | |
| 6 | 1 | 41 | 0.6843896155 | Henry Cohn, 2024 | |
| 6 | 1 | 42 | 0.6810759859 | Henry Cohn, 2024 | |
| 6 | 1 | 43 | 0.6775225130 | ||
| 6 | 1 | 44 | 0.6730735629 | ||
| 6 | 1 | 45 | 0.6709820470 | Henry Cohn, 2025 | |
| 6 | 1 | 46 | 0.6707778161 | ||
| 6 | 1 | 47 | 0.6668214796 | Henry Cohn, 2025 | |
| 6 | 1 | 48 | 0.6643421396 | Henry Cohn, 2025 | |
| 6 | 1 | 49 | 0.6628431715 | Henry Cohn, 2024 | |
| 6 | 1 | 50 | 0.6597970822 | Henry Cohn, 2024 | |
| 6 | 1 | 51 | 0.6573685006 | Henry Cohn, 2025 | |
| 6 | 1 | 52 | 0.6549928217 | Henry Cohn, 2025 | |
| 6 | 1 | 53 | 0.6518862854 | Henry Cohn, 2025 | |
| 6 | 1 | 54 | 0.6472993195 | Henry Cohn, 2024 | |
| 6 | 1 | 55 | 0.6458906248 | Henry Cohn, 2024 | |
| 6 | 1 | 56 | 0.6445726790 | Henry Cohn, 2024 | |
| 6 | 1 | 57 | 0.6422717420 | Henry Cohn, 2025 | |
| 6 | 1 | 58 | 0.6414203744 | Henry Cohn, 2024 | |
| 6 | 1 | 59 | 0.6408108766 | ||
| 6 | 1 | 60 | 0.6408108766 | ||
| 6 | 1 | 61 | 0.6288607578 | ||
| 6 | 1 | 62 | 0.6259241568 | Henry Cohn, 2025 | |
| 6 | 1 | 63 | 0.6249999999 | ||
| 6 | 1 | 64 | 0.6153741569 | Henry Cohn, 2024 | |
| 6 | 1 | 65 | 0.6105682359 | ||
| 6 | 1 | 66 | 0.6074060558 | Henry Cohn, 2024 | |
| 6 | 1 | 67 | 0.6042661694 | ||
| 6 | 1 | 68 | 0.6007281916 | Henry Cohn, 2024 | |
| 6 | 1 | 69 | 0.5970054012 | ||
| 6 | 1 | 70 | 0.5934453317 | ||
| 6 | 1 | 71 | 0.5902148793 | ||
| 6 | 1 | 72 | 0.5871179693 | Henry Cohn, 2024 | |
| 6 | 1 | 73 | 0.5839833402 | ||
| 6 | 1 | 74 | 0.5815383479 | Henry Cohn, 2024 | |
| 6 | 1 | 75 | 0.5783753807 | ||
| 6 | 1 | 76 | 0.5747784532 | ||
| 6 | 1 | 77 | 0.5717458998 | ||
| 6 | 1 | 78 | 0.5683706678 | Henry Cohn, 2024 | |
| 6 | 1 | 79 | 0.5654040319 | ||
| 6 | 1 | 80 | 0.5626916126 | ||
| 6 | 1 | 81 | 0.5597843410 | ||
| 6 | 1 | 82 | 0.5570452954 | ||
| 6 | 1 | 83 | 0.5542475706 | ||
| 6 | 1 | 84 | 0.5516596619 | ||
| 6 | 1 | 85 | 0.5496095748 | ||
| 6 | 1 | 86 | 0.5466722586 | ||
| 6 | 1 | 87 | 0.5443435724 | ||
| 6 | 1 | 88 | 0.5423055738 | ||
| 6 | 1 | 89 | 0.5410890736 | ||
| 6 | 1 | 90 | 0.5403777598 | ||
| 6 | 1 | 91 | 0.5356260482 | ||
| 6 | 1 | 92 | 0.5334132190 | ||
| 6 | 1 | 93 | 0.5314755905 | ||
| 6 | 1 | 94 | 0.5295919736 | ||
| 6 | 1 | 95 | 0.5280243126 | ||
| 6 | 1 | 96 | 0.5262807474 | ||
| 6 | 1 | 97 | 0.5253380392 | ||
| 6 | 1 | 98 | 0.5246693560 | ||
| 6 | 1 | 99 | 0.5234407485 | ||
| 6 | 1 | 100 | 0.5225120511 | ||
| ∗ 6 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound [4] |
| ∗ 6 | 2 | 4 | 1.7777777777 | 1.7777777778 | tight bound [4] |
| ∗ 6 | 2 | 5 | 1.6666666666 | 1.6666666667 | tight bound [4] |
| ∗ 6 | 2 | 6 | 1.5999999999 | 1.6000000000 | tight bound [4] |
| ∗ 6 | 2 | 7 | 1.5555555555 | 1.5555555556 | tight bound [4] |
| ∗ 6 | 2 | 8 | 1.5238095238 | 1.5238095239 | tight bound [4] |
| ∗ 6 | 2 | 9 | 1.4999999999 | 1.5000000000 | tight bound [5] |
| ∗ 6 | 2 | 10 | 1.4814814814 | 1.4814814815 | tight bound [4] |
| ∗ 6 | 2 | 11 | 1.4666666666 | 1.4666666667 | tight bound [4] |
| ∗ 6 | 2 | 12 | 1.4545454545 | 1.4545454546 | tight bound [4] |
| ∗ 6 | 2 | 13 | 1.4444444444 | 1.4444444445 | tight bound [4] |
| ∗ 6 | 2 | 14 | 1.4358974358 | 1.4358974359 | tight bound [4] |
| 6 | 2 | 15 | 1.4285668598 | 1.4285714286 | |
| 6 | 2 | 16 | 1.4210084212 | 1.4222222223 | |
| 6 | 2 | 17 | 1.4127250337 | 1.4166666667 | |
| 6 | 2 | 18 | 1.4047583969 | 1.4117647059 | |
| 6 | 2 | 19 | 1.3948290755 | 1.4074074075 | |
| 6 | 2 | 20 | 1.3887598649 | 1.4035087720 | |
| 6 | 2 | 21 | 1.3821363792 | 1.4000000000 | |
| ∗ 6 | 2 | 22 | 1.3333333333 | 1.3333333334 | |
| ∗ 6 | 2 | 23 | 1.3333333333 | 1.3333333334 | |
| 6 | 2 | 24 | 1.3325968962 | 1.3333333334 | |
| 6 | 2 | 25 | 1.3229201727 | 1.3333333334 | |
| 6 | 2 | 26 | 1.3151115938 | 1.3333333334 | |
| 6 | 2 | 27 | 1.3071354482 | 1.3333333334 | |
| 6 | 2 | 28 | 1.2987494813 | 1.3333333334 | |
| 6 | 2 | 29 | 1.2887480533 | 1.3333333334 | |
| 6 | 2 | 30 | 1.2803723341 | 1.3333333334 | |
| 6 | 2 | 31 | 1.2683924399 | 1.3333333334 | |
| 6 | 2 | 32 | 1.2590136697 | 1.3333333334 | |
| 6 | 2 | 33 | 1.2525697988 | 1.3333333334 | |
| 6 | 2 | 34 | 1.2447031126 | 1.3333333334 | |
| 6 | 2 | 35 | 1.2430079033 | 1.3333333334 | |
| 6 | 2 | 36 | 1.2344708713 | 1.3333333334 | |
| 6 | 2 | 37 | 1.2276166051 | 1.3333333334 | |
| 6 | 2 | 38 | 1.2239376175 | 1.3333333334 | |
| 6 | 2 | 39 | 1.2205828463 | 1.3333333334 | |
| 6 | 2 | 40 | 1.2149153244 | 1.3333333334 | |
| 6 | 2 | 41 | 1.2115353844 | ||
| 6 | 2 | 42 | 1.2079375907 | ||
| 6 | 2 | 43 | 1.2036740337 | ||
| 6 | 2 | 44 | 1.2007477223 | ||
| 6 | 2 | 45 | 1.1970435093 | ||
| 6 | 2 | 46 | 1.1955236435 | ||
| 6 | 2 | 47 | 1.1927054640 | ||
| 6 | 2 | 48 | 1.1907500968 | ||
| 6 | 2 | 49 | 1.1874860499 | ||
| 6 | 2 | 50 | 1.1841430338 | ||
| 6 | 2 | 51 | 1.1816449842 | ||
| 6 | 2 | 52 | 1.1790350370 | ||
| 6 | 2 | 53 | 1.1752417288 | ||
| 6 | 2 | 54 | 1.1726203520 | ||
| 6 | 2 | 55 | 1.1709677900 | ||
| 6 | 2 | 56 | 1.1686951904 | ||
| 6 | 2 | 57 | 1.1669485036 | ||
| 6 | 2 | 58 | 1.1646036685 | ||
| 6 | 2 | 59 | 1.1636012015 | ||
| 6 | 2 | 60 | 1.1605380939 | ||
| 6 | 2 | 61 | 1.1592565267 | ||
| 6 | 2 | 62 | 1.1563685263 | ||
| 6 | 2 | 63 | 1.1534349093 | ||
| 6 | 2 | 64 | 1.1502193651 | ||
| 6 | 2 | 65 | 1.1462940857 | ||
| 6 | 2 | 66 | 1.1440936287 | ||
| 6 | 2 | 67 | 1.1405648287 | ||
| 6 | 2 | 68 | 1.1385033505 | ||
| 6 | 2 | 69 | 1.1353800766 | ||
| 6 | 2 | 70 | 1.1325487156 | ||
| 6 | 2 | 71 | 1.1317589395 | ||
| 6 | 2 | 72 | 1.1307823543 | ||
| 6 | 2 | 73 | 1.1292234424 | ||
| 6 | 2 | 74 | 1.1283378031 | ||
| 6 | 2 | 75 | 1.1269926838 | ||
| 6 | 2 | 76 | 1.1217945827 | ||
| 6 | 2 | 77 | 1.1167335916 | ||
| 6 | 2 | 78 | 1.1128464512 | ||
| 6 | 2 | 79 | 1.1085974370 | ||
| 6 | 2 | 80 | 1.1054673384 | ||
| 6 | 2 | 81 | 1.1023649207 | ||
| 6 | 2 | 82 | 1.0994449841 | ||
| 6 | 2 | 83 | 1.0968005857 | ||
| 6 | 2 | 84 | 1.0948369706 | ||
| 6 | 2 | 85 | 1.0932604315 | ||
| 6 | 2 | 86 | 1.0899901239 | ||
| 6 | 2 | 87 | 1.0877593288 | ||
| 6 | 2 | 88 | 1.0854576425 | ||
| 6 | 2 | 89 | 1.0832085511 | ||
| 6 | 2 | 90 | 1.0813145841 | ||
| 6 | 2 | 91 | 1.0787028526 | ||
| 6 | 2 | 92 | 1.0774951976 | ||
| 6 | 2 | 93 | 1.0749489149 | ||
| 6 | 2 | 94 | 1.0724303637 | ||
| 6 | 2 | 95 | 1.0710584338 | ||
| 6 | 2 | 96 | 1.0681970178 | ||
| 6 | 2 | 97 | 1.0663204323 | ||
| 6 | 2 | 98 | 1.0642587442 | ||
| 6 | 2 | 99 | 1.0623180796 | ||
| 6 | 2 | 100 | 1.0600574437 | ||
| ∗ 6 | 3 | 3 | 2.2499999999 | 2.2500000000 | tight bound [4] |
| ∗ 6 | 3 | 4 | 1.9999999999 | 2.0000000000 | tight bound [4] |
| ∗ 6 | 3 | 5 | 1.8749999999 | 1.8750000000 | tight bound [4] |
| ∗ 6 | 3 | 6 | 1.7999999999 | 1.8000000000 | tight bound [4] |
| ∗ 6 | 3 | 7 | 1.7499999999 | 1.7500000000 | tight bound [4] |
| ∗ 6 | 3 | 8 | 1.7142857142 | 1.7142857143 | tight bound [4] |
| ∗ 6 | 3 | 9 | 1.6874999999 | 1.6875000000 | tight bound [4] |
| ∗ 6 | 3 | 10 | 1.6666666666 | 1.6666666667 | tight bound [4] |
| ∗ 6 | 3 | 11 | 1.6499999999 | 1.6500000000 | tight bound [4] |
| ∗ 6 | 3 | 12 | 1.6363636363 | 1.6363636364 | tight bound [4] |
| ∗ 6 | 3 | 13 | 1.6249999999 | 1.6250000000 | tight bound [4] |
| ∗ 6 | 3 | 14 | 1.6153846153 | 1.6153846154 | tight bound [4] |
| ∗ 6 | 3 | 15 | 1.6071428571 | 1.6071428572 | tight bound [4] |
| ∗ 6 | 3 | 16 | 1.5999999999 | 1.6000000000 | tight bound [4] |
| 6 | 3 | 17 | 1.5937499963 | 1.5937500000 | unclear whether bound is tight |
| 6 | 3 | 18 | 1.5881502528 | 1.5882352942 | |
| 6 | 3 | 19 | 1.5818405394 | 1.5833333334 | |
| 6 | 3 | 20 | 1.5780693377 | 1.5789473685 | |
| 6 | 3 | 21 | 1.5735218412 | 1.5750000000 | |
| ∗ 6 | 3 | 22 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 23 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 24 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 25 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 26 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 27 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 28 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 29 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 30 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 31 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 32 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 33 | 1.4999999999 | 1.5000000000 | |
| ∗ 6 | 3 | 34 | 1.4999999999 | 1.5000000000 | |
| 6 | 3 | 35 | 1.4999790749 | 1.5000000000 | |
| 6 | 3 | 36 | 1.4999749561 | 1.5000000000 | |
| 6 | 3 | 37 | 1.4998599873 | 1.5000000000 | |
| 6 | 3 | 38 | 1.4998288205 | 1.5000000000 | |
| 6 | 3 | 39 | 1.4997976429 | 1.5000000000 | |
| 6 | 3 | 40 | 1.4997712615 | 1.5000000000 | |
| 6 | 3 | 41 | 1.4297222744 | ||
| 6 | 3 | 42 | 1.4231484347 | ||
| 6 | 3 | 43 | 1.3975595909 | ||
| 6 | 3 | 44 | 1.3894247196 | ||
| 6 | 3 | 45 | 1.3772905258 | ||
| 6 | 3 | 46 | 1.3696725240 | ||
| 6 | 3 | 47 | 1.3634363253 | ||
| 6 | 3 | 48 | 1.3578030702 | ||
| 6 | 3 | 49 | 1.3542944243 | ||
| 6 | 3 | 50 | 1.3500545862 | ||
| 6 | 3 | 51 | 1.3459853355 | ||
| 6 | 3 | 52 | 1.3442326620 | ||
| 6 | 3 | 53 | 1.3419575414 | ||
| 6 | 3 | 54 | 1.3399765372 | ||
| 6 | 3 | 55 | 1.3381181039 | ||
| 6 | 3 | 56 | 1.3359596171 | ||
| 6 | 3 | 57 | 1.3338283840 | ||
| 6 | 3 | 58 | 1.3323120718 | ||
| 6 | 3 | 59 | 1.3306292939 | ||
| 6 | 3 | 60 | 1.3288903369 | ||
| 6 | 3 | 61 | 1.3263929129 | ||
| 6 | 3 | 62 | 1.3228485128 | ||
| 6 | 3 | 63 | 1.3195098424 | ||
| 6 | 3 | 64 | 1.3159623462 | ||
| 6 | 3 | 65 | 1.3124920897 | ||
| 6 | 3 | 66 | 1.3099925448 | ||
| 6 | 3 | 67 | 1.3057536632 | ||
| 6 | 3 | 68 | 1.3031134007 | ||
| 6 | 3 | 69 | 1.2997741461 | ||
| 6 | 3 | 70 | 1.2979919058 | ||
| 6 | 3 | 71 | 1.2974643049 | ||
| 6 | 3 | 72 | 1.2941627120 | ||
| 6 | 3 | 73 | 1.2926475323 | ||
| 6 | 3 | 74 | 1.2906178794 | ||
| 6 | 3 | 75 | 1.2883858393 | ||
| 6 | 3 | 76 | 1.2860607212 | ||
| 6 | 3 | 77 | 1.2837399706 | ||
| 6 | 3 | 78 | 1.2820332874 | ||
| 6 | 3 | 79 | 1.2794045677 | ||
| 6 | 3 | 80 | 1.2774513927 | ||
| 6 | 3 | 81 | 1.2750874777 | ||
| 6 | 3 | 82 | 1.2733119875 | ||
| 6 | 3 | 83 | 1.2718321581 | ||
| 6 | 3 | 84 | 1.2699317880 | ||
| 6 | 3 | 85 | 1.2678980788 | ||
| 6 | 3 | 86 | 1.2663115061 | ||
| 6 | 3 | 87 | 1.2645392981 | ||
| 6 | 3 | 88 | 1.2626284684 | ||
| 6 | 3 | 89 | 1.2605294603 | ||
| 6 | 3 | 90 | 1.2587028763 | ||
| 6 | 3 | 91 | 1.2570913180 | ||
| 6 | 3 | 92 | 1.2547466351 | ||
| 6 | 3 | 93 | 1.2514357315 | ||
| 6 | 3 | 94 | 1.2488921230 | ||
| 6 | 3 | 95 | 1.2462640722 | ||
| 6 | 3 | 96 | 1.2433375741 | ||
| 6 | 3 | 97 | 1.2408008155 | ||
| 6 | 3 | 98 | 1.2381932424 | ||
| 6 | 3 | 99 | 1.2357149907 | ||
| 6 | 3 | 100 | 1.2333650196 | ||
| ∗ 7 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 7 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 7 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 7 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 7 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 7 | 1 | 8 | 0.9795918367 | 0.9795918368 | tight bound |
| 7 | 1 | 9 | 0.9599999999 | 0.9642857143 | |
| 7 | 1 | 10 | 0.9442719099 | 0.9523809524 | |
| 7 | 1 | 11 | 0.9331689892 | 0.9428571429 | |
| 7 | 1 | 12 | 0.9256198347 | 0.9350649351 | |
| 7 | 1 | 13 | 0.9230769230 | 0.9285714286 | |
| ∗ 7 | 1 | 14 | 0.9230769230 | 0.9230769231 | tight bound |
| 7 | 1 | 15 | 0.9000282686 | 0.9183673470 | Henry Cohn [2] |
| 7 | 1 | 16 | 0.8938560428 | 0.9142857143 | Henry Cohn [3] |
| 7 | 1 | 17 | 0.8897094111 | 0.9107142858 | Henry Cohn, 2023 |
| 7 | 1 | 18 | 0.8891525949 | 0.9075630253 | Henry Cohn, 2024 |
| 7 | 1 | 19 | 0.8888888888 | 0.9047619048 | |
| 7 | 1 | 20 | 0.8888888888 | 0.9022556391 | |
| 7 | 1 | 21 | 0.8888888888 | 0.9000000000 | |
| 7 | 1 | 22 | 0.8888888888 | 0.8979591837 | |
| 7 | 1 | 23 | 0.8888888888 | 0.8961038962 | |
| 7 | 1 | 24 | 0.8888888888 | 0.8944099379 | |
| 7 | 1 | 25 | 0.8888888888 | 0.8928571429 | |
| 7 | 1 | 26 | 0.8888888888 | 0.8914285715 | |
| 7 | 1 | 27 | 0.8888888888 | 0.8901098902 | |
| ∗ 7 | 1 | 28 | 0.8888888888 | 0.8888888889 | tight bound |
| 7 | 1 | 29 | 0.8445312981 | 0.8571428572 | |
| 7 | 1 | 30 | 0.8313923657 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 31 | 0.8240492092 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 32 | 0.8176605309 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 33 | 0.8163265306 | 0.8571428572 | |
| 7 | 1 | 34 | 0.8163265306 | 0.8571428572 | |
| 7 | 1 | 35 | 0.8163265306 | 0.8571428572 | |
| 7 | 1 | 36 | 0.8163265306 | 0.8571428572 | |
| 7 | 1 | 37 | 0.7850659657 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 38 | 0.7816698233 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 39 | 0.7753229524 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 40 | 0.7705692097 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 41 | 0.7673681854 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 42 | 0.7623626256 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 43 | 0.7578083055 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 44 | 0.7554575138 | 0.8571428572 | Henry Cohn, 2024 |
| 7 | 1 | 45 | 0.7534439276 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 46 | 0.7516851450 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 47 | 0.7506663684 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 48 | 0.7501932632 | 0.8571428572 | Henry Cohn, 2025 |
| 7 | 1 | 49 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 50 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 51 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 52 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 53 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 54 | 0.7499999999 | 0.8571428572 | |
| 7 | 1 | 55 | 0.7499999999 | ||
| 7 | 1 | 56 | 0.7499999999 | ||
| 7 | 1 | 57 | 0.7499999999 | ||
| 7 | 1 | 58 | 0.7499999999 | ||
| 7 | 1 | 59 | 0.7499999999 | ||
| 7 | 1 | 60 | 0.7499999999 | ||
| 7 | 1 | 61 | 0.7499999999 | ||
| 7 | 1 | 62 | 0.7499999999 | ||
| 7 | 1 | 63 | 0.7499999999 | ||
| 7 | 1 | 64 | 0.7272727272 | ||
| 7 | 1 | 65 | 0.7101196278 | Henry Cohn, 2024 | |
| 7 | 1 | 66 | 0.7092457690 | Henry Cohn, 2024 | |
| 7 | 1 | 67 | 0.7026520710 | ||
| 7 | 1 | 68 | 0.6996862692 | ||
| 7 | 1 | 69 | 0.6976109515 | ||
| 7 | 1 | 70 | 0.6953607564 | Henry Cohn, 2024 | |
| 7 | 1 | 71 | 0.6929495862 | ||
| 7 | 1 | 72 | 0.6922523975 | Henry Cohn, 2024 | |
| 7 | 1 | 73 | 0.6905244807 | ||
| 7 | 1 | 74 | 0.6893879402 | Henry Cohn, 2024 | |
| 7 | 1 | 75 | 0.6884389065 | ||
| 7 | 1 | 76 | 0.6879253343 | ||
| 7 | 1 | 77 | 0.6854109241 | ||
| 7 | 1 | 78 | 0.6848589381 | Henry Cohn, 2024 | |
| 7 | 1 | 79 | 0.6829044957 | ||
| 7 | 1 | 80 | 0.6821181597 | ||
| 7 | 1 | 81 | 0.6818728582 | ||
| 7 | 1 | 82 | 0.6789136560 | ||
| 7 | 1 | 83 | 0.6779723038 | ||
| 7 | 1 | 84 | 0.6761564392 | ||
| 7 | 1 | 85 | 0.6740741367 | ||
| 7 | 1 | 86 | 0.6692497584 | ||
| 7 | 1 | 87 | 0.6690022597 | ||
| 7 | 1 | 88 | 0.6684937216 | ||
| 7 | 1 | 89 | 0.6680051825 | ||
| 7 | 1 | 90 | 0.6677412055 | ||
| 7 | 1 | 91 | 0.6666666666 | ||
| 7 | 1 | 92 | 0.6501548456 | ||
| 7 | 1 | 93 | 0.6481425124 | ||
| 7 | 1 | 94 | 0.6464885044 | ||
| 7 | 1 | 95 | 0.6456776808 | ||
| 7 | 1 | 96 | 0.6427894602 | ||
| 7 | 1 | 97 | 0.6394031665 | ||
| 7 | 1 | 98 | 0.6371403693 | ||
| 7 | 1 | 99 | 0.6351707549 | ||
| 7 | 1 | 100 | 0.6328046273 | ||
| ∗ 7 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| 7 | 2 | 4 | 1.8888888888 | 1.9047619048 | |
| 7 | 2 | 5 | 1.7853996980 | 1.7857142858 | |
| ∗ 7 | 2 | 6 | 1.7142857142 | 1.7142857143 | tight bound [4] |
| ∗ 7 | 2 | 7 | 1.6666666666 | 1.6666666667 | tight bound [4] |
| ∗ 7 | 2 | 8 | 1.6326530612 | 1.6326530613 | tight bound [4] |
| ∗ 7 | 2 | 9 | 1.6071428571 | 1.6071428572 | tight bound [4] |
| ∗ 7 | 2 | 10 | 1.5873015873 | 1.5873015874 | tight bound [4] |
| ∗ 7 | 2 | 11 | 1.5714285714 | 1.5714285715 | tight bound [4] |
| ∗ 7 | 2 | 12 | 1.5584415584 | 1.5584415585 | tight bound [4] |
| ∗ 7 | 2 | 13 | 1.5476190476 | 1.5476190477 | tight bound [4] |
| ∗ 7 | 2 | 14 | 1.5384615384 | 1.5384615385 | tight bound [4] |
| ∗ 7 | 2 | 15 | 1.5306122448 | 1.5306122449 | tight bound [4] |
| ∗ 7 | 2 | 16 | 1.5238095238 | 1.5238095239 | tight bound [4] |
| ∗ 7 | 2 | 17 | 1.5178571428 | 1.5178571429 | tight bound [4] |
| 7 | 2 | 18 | 1.5126049647 | 1.5126050421 | unclear whether bound is tight |
| 7 | 2 | 19 | 1.5078135777 | 1.5079365080 | |
| 7 | 2 | 20 | 1.5025651961 | 1.5037593985 | |
| 7 | 2 | 21 | 1.4986698794 | 1.5000000000 | |
| 7 | 2 | 22 | 1.4911646318 | 1.4965986395 | |
| 7 | 2 | 23 | 1.4858572869 | 1.4935064936 | |
| 7 | 2 | 24 | 1.4789664832 | 1.4906832299 | |
| 7 | 2 | 25 | 1.4724778886 | 1.4880952381 | |
| 7 | 2 | 26 | 1.4666498991 | 1.4857142858 | |
| 7 | 2 | 27 | 1.4606000326 | 1.4835164836 | |
| 7 | 2 | 28 | 1.4530805455 | 1.4814814815 | |
| ∗ 7 | 2 | 29 | 1.4285714285 | 1.4285714286 | |
| 7 | 2 | 30 | 1.4234168210 | 1.4285714286 | |
| 7 | 2 | 31 | 1.4167413920 | 1.4285714286 | |
| 7 | 2 | 32 | 1.4106172456 | 1.4285714286 | |
| 7 | 2 | 33 | 1.4038294444 | 1.4285714286 | |
| 7 | 2 | 34 | 1.3978005668 | 1.4285714286 | |
| 7 | 2 | 35 | 1.3915140837 | 1.4285714286 | |
| 7 | 2 | 36 | 1.3846616119 | 1.4285714286 | |
| 7 | 2 | 37 | 1.3787964945 | 1.4285714286 | |
| 7 | 2 | 38 | 1.3723186833 | 1.4285714286 | |
| 7 | 2 | 39 | 1.3666505200 | 1.4285714286 | |
| 7 | 2 | 40 | 1.3605996315 | 1.4285714286 | |
| 7 | 2 | 41 | 1.3574900911 | 1.4285714286 | |
| 7 | 2 | 42 | 1.3550346662 | 1.4285714286 | |
| 7 | 2 | 43 | 1.3449020718 | 1.4285714286 | |
| 7 | 2 | 44 | 1.3407058526 | 1.4285714286 | |
| 7 | 2 | 45 | 1.3356536494 | 1.4285714286 | |
| 7 | 2 | 46 | 1.3321216420 | 1.4285714286 | |
| 7 | 2 | 47 | 1.3267186601 | 1.4285714286 | |
| 7 | 2 | 48 | 1.3231954071 | 1.4285714286 | |
| 7 | 2 | 49 | 1.3209340300 | 1.4285714286 | |
| 7 | 2 | 50 | 1.3150008002 | 1.4285714286 | |
| 7 | 2 | 51 | 1.3111594033 | 1.4285714286 | |
| 7 | 2 | 52 | 1.3072463731 | 1.4285714286 | |
| 7 | 2 | 53 | 1.3039771601 | 1.4285714286 | |
| 7 | 2 | 54 | 1.3005373239 | 1.4285714286 | |
| 7 | 2 | 55 | 1.2977549116 | ||
| 7 | 2 | 56 | 1.2951504509 | ||
| 7 | 2 | 57 | 1.2908080891 | ||
| 7 | 2 | 58 | 1.2877363684 | ||
| 7 | 2 | 59 | 1.2848918218 | ||
| 7 | 2 | 60 | 1.2816993374 | ||
| 7 | 2 | 61 | 1.2787261110 | ||
| 7 | 2 | 62 | 1.2762435035 | ||
| 7 | 2 | 63 | 1.2741915056 | ||
| 7 | 2 | 64 | 1.2709640809 | ||
| 7 | 2 | 65 | 1.2686289333 | ||
| 7 | 2 | 66 | 1.2661430553 | ||
| 7 | 2 | 67 | 1.2639313864 | ||
| 7 | 2 | 68 | 1.2613220241 | ||
| 7 | 2 | 69 | 1.2593780842 | ||
| 7 | 2 | 70 | 1.2570428981 | ||
| 7 | 2 | 71 | 1.2550353889 | ||
| 7 | 2 | 72 | 1.2525900339 | ||
| 7 | 2 | 73 | 1.2503852344 | ||
| 7 | 2 | 74 | 1.2481794391 | ||
| 7 | 2 | 75 | 1.2461449969 | ||
| 7 | 2 | 76 | 1.2439461645 | ||
| 7 | 2 | 77 | 1.2424395212 | ||
| 7 | 2 | 78 | 1.2403264525 | ||
| 7 | 2 | 79 | 1.2385057683 | ||
| 7 | 2 | 80 | 1.2368075509 | ||
| 7 | 2 | 81 | 1.2347641678 | ||
| 7 | 2 | 82 | 1.2329815570 | ||
| 7 | 2 | 83 | 1.2312377095 | ||
| 7 | 2 | 84 | 1.2295558152 | ||
| 7 | 2 | 85 | 1.2279243483 | ||
| 7 | 2 | 86 | 1.2263595006 | ||
| 7 | 2 | 87 | 1.2247949249 | ||
| 7 | 2 | 88 | 1.2231005224 | ||
| 7 | 2 | 89 | 1.2218114308 | ||
| 7 | 2 | 90 | 1.2204226022 | ||
| 7 | 2 | 91 | 1.2186197730 | ||
| 7 | 2 | 92 | 1.2170420393 | ||
| 7 | 2 | 93 | 1.2153674979 | ||
| 7 | 2 | 94 | 1.2138172699 | ||
| 7 | 2 | 95 | 1.2121348994 | ||
| 7 | 2 | 96 | 1.2109491523 | ||
| 7 | 2 | 97 | 1.2093494870 | ||
| 7 | 2 | 98 | 1.2079309969 | ||
| 7 | 2 | 99 | 1.2068681964 | ||
| 7 | 2 | 100 | 1.2049910656 | ||
| 7 | 3 | 3 | 2.4999999999 | 2.5714285715 | |
| ∗ 7 | 3 | 4 | 2.2857142857 | 2.2857142858 | tight bound [4] |
| ∗ 7 | 3 | 5 | 2.1428571428 | 2.1428571429 | tight bound [4] |
| ∗ 7 | 3 | 6 | 2.0571428571 | 2.0571428572 | tight bound [4] |
| ∗ 7 | 3 | 7 | 1.9999999999 | 2.0000000000 | tight bound [4] |
| ∗ 7 | 3 | 8 | 1.9591836734 | 1.9591836735 | tight bound [4] |
| ∗ 7 | 3 | 9 | 1.9285714285 | 1.9285714286 | tight bound [4] |
| ∗ 7 | 3 | 10 | 1.9047619047 | 1.9047619048 | tight bound [4] |
| ∗ 7 | 3 | 11 | 1.8857142857 | 1.8857142858 | tight bound [4] |
| ∗ 7 | 3 | 12 | 1.8701298701 | 1.8701298702 | tight bound [4] |
| ∗ 7 | 3 | 13 | 1.8571428571 | 1.8571428572 | tight bound [4] |
| ∗ 7 | 3 | 14 | 1.8461538461 | 1.8461538462 | tight bound [4] |
| ∗ 7 | 3 | 15 | 1.8367346938 | 1.8367346939 | tight bound [4] |
| ∗ 7 | 3 | 16 | 1.8285714285 | 1.8285714286 | tight bound [4] |
| ∗ 7 | 3 | 17 | 1.8214285714 | 1.8214285715 | tight bound [4] |
| ∗ 7 | 3 | 18 | 1.8151260504 | 1.8151260505 | tight bound [4] |
| ∗ 7 | 3 | 19 | 1.8095238095 | 1.8095238096 | tight bound [4] |
| ∗ 7 | 3 | 20 | 1.8045112781 | 1.8045112782 | tight bound [4] |
| ∗ 7 | 3 | 21 | 1.7999999999 | 1.8000000000 | tight bound [4] |
| ∗ 7 | 3 | 22 | 1.7959183673 | 1.7959183674 | tight bound [4] |
| 7 | 3 | 23 | 1.7922077630 | 1.7922077923 | unclear whether bound is tight |
| 7 | 3 | 24 | 1.7885259141 | 1.7888198758 | |
| 7 | 3 | 25 | 1.7845144676 | 1.7857142858 | |
| 7 | 3 | 26 | 1.7802988168 | 1.7828571429 | |
| 7 | 3 | 27 | 1.7777777777 | 1.7802197803 | |
| ∗ 7 | 3 | 28 | 1.7777777777 | 1.7777777778 | tight bound [5] |
| ∗ 7 | 3 | 29 | 1.7142857142 | 1.7142857143 | |
| ∗ 7 | 3 | 30 | 1.7142857142 | 1.7142857143 | |
| ∗ 7 | 3 | 31 | 1.7142857142 | 1.7142857143 | |
| 7 | 3 | 32 | 1.7123818065 | 1.7142857143 | |
| 7 | 3 | 33 | 1.7090579490 | 1.7142857143 | |
| 7 | 3 | 34 | 1.7045536491 | 1.7142857143 | |
| 7 | 3 | 35 | 1.6993966165 | 1.7142857143 | |
| 7 | 3 | 36 | 1.6940796385 | 1.7142857143 | |
| 7 | 3 | 37 | 1.6853688082 | 1.7142857143 | |
| 7 | 3 | 38 | 1.6782858851 | 1.7142857143 | |
| 7 | 3 | 39 | 1.6724829492 | 1.7142857143 | |
| 7 | 3 | 40 | 1.6671276045 | 1.7142857143 | |
| 7 | 3 | 41 | 1.6622964593 | 1.7142857143 | |
| 7 | 3 | 42 | 1.6599721328 | 1.7142857143 | |
| 7 | 3 | 43 | 1.6530488721 | 1.7142857143 | |
| 7 | 3 | 44 | 1.6485675628 | 1.7142857143 | |
| 7 | 3 | 45 | 1.6447847108 | 1.7142857143 | |
| 7 | 3 | 46 | 1.6401963991 | 1.7142857143 | |
| 7 | 3 | 47 | 1.6359455404 | 1.7142857143 | |
| 7 | 3 | 48 | 1.6318722186 | 1.7142857143 | |
| 7 | 3 | 49 | 1.6286298553 | 1.7142857143 | |
| 7 | 3 | 50 | 1.6243991404 | 1.7142857143 | |
| 7 | 3 | 51 | 1.6205530337 | 1.7142857143 | |
| 7 | 3 | 52 | 1.6166859122 | 1.7142857143 | |
| 7 | 3 | 53 | 1.6126345779 | 1.7142857143 | |
| 7 | 3 | 54 | 1.6091095014 | 1.7142857143 | |
| 7 | 3 | 55 | 1.6053922212 | ||
| 7 | 3 | 56 | 1.6018504077 | ||
| 7 | 3 | 57 | 1.5988670306 | ||
| 7 | 3 | 58 | 1.5951321828 | ||
| 7 | 3 | 59 | 1.5916167672 | ||
| 7 | 3 | 60 | 1.5891343332 | ||
| 7 | 3 | 61 | 1.5858780607 | ||
| 7 | 3 | 62 | 1.5822464688 | ||
| 7 | 3 | 63 | 1.5792334760 | ||
| 7 | 3 | 64 | 1.5766033063 | ||
| 7 | 3 | 65 | 1.5739901872 | ||
| 7 | 3 | 66 | 1.5704264419 | ||
| 7 | 3 | 67 | 1.5672619017 | ||
| 7 | 3 | 68 | 1.5643389046 | ||
| 7 | 3 | 69 | 1.5613224723 | ||
| 7 | 3 | 70 | 1.5584631552 | ||
| 7 | 3 | 71 | 1.5555870749 | ||
| 7 | 3 | 72 | 1.5524832564 | ||
| 7 | 3 | 73 | 1.5493477805 | ||
| 7 | 3 | 74 | 1.5464928374 | ||
| 7 | 3 | 75 | 1.5445045976 | ||
| 7 | 3 | 76 | 1.5410845074 | ||
| 7 | 3 | 77 | 1.5393865819 | ||
| 7 | 3 | 78 | 1.5358010907 | ||
| 7 | 3 | 79 | 1.5327161199 | ||
| 7 | 3 | 80 | 1.5302183992 | ||
| 7 | 3 | 81 | 1.5277618493 | ||
| 7 | 3 | 82 | 1.5251803048 | ||
| 7 | 3 | 83 | 1.5225572939 | ||
| 7 | 3 | 84 | 1.5199230998 | ||
| 7 | 3 | 85 | 1.5176187665 | ||
| 7 | 3 | 86 | 1.5157726523 | ||
| 7 | 3 | 87 | 1.5132902028 | ||
| 7 | 3 | 88 | 1.5112045823 | ||
| 7 | 3 | 89 | 1.5088923199 | ||
| 7 | 3 | 90 | 1.5067859785 | ||
| 7 | 3 | 91 | 1.5043159181 | ||
| 7 | 3 | 92 | 1.5026853705 | ||
| 7 | 3 | 93 | 1.5003138772 | ||
| 7 | 3 | 94 | 1.4985597338 | ||
| 7 | 3 | 95 | 1.4965800606 | ||
| 7 | 3 | 96 | 1.4947515620 | ||
| 7 | 3 | 97 | 1.4926248315 | ||
| 7 | 3 | 98 | 1.4907987931 | ||
| 7 | 3 | 99 | 1.4891349922 | ||
| 7 | 3 | 100 | 1.4870328370 | ||
| ∗ 8 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 8 | 1 | 9 | 0.9843749999 | 0.9843750000 | tight bound |
| 8 | 1 | 10 | 0.9666046313 | 0.9722222223 | |
| 8 | 1 | 11 | 0.9558423333 | 0.9625000000 | Henry Cohn [2] |
| 8 | 1 | 12 | 0.9463324958 | 0.9545454546 | |
| 8 | 1 | 13 | 0.9428498176 | 0.9479166667 | Henry Cohn [2] |
| 8 | 1 | 14 | 0.9333173024 | 0.9423076924 | |
| 8 | 1 | 15 | 0.9271187957 | 0.9375000000 | Henry Cohn [2] |
| 8 | 1 | 16 | 0.9249505911 | 0.9333333334 | |
| 8 | 1 | 17 | 0.9158776325 | 0.9296875000 | Henry Cohn, 2023 |
| 8 | 1 | 18 | 0.9120270918 | 0.9264705883 | |
| 8 | 1 | 19 | 0.9052829527 | 0.9236111112 | |
| 8 | 1 | 20 | 0.9011031374 | 0.9210526316 | Henry Cohn, 2025 |
| 8 | 1 | 21 | 0.8977598901 | 0.9187500000 | Henry Cohn, 2025 |
| 8 | 1 | 22 | 0.8950594747 | 0.9166666667 | |
| 8 | 1 | 23 | 0.8915606334 | 0.9147727273 | Henry Cohn, 2025 |
| 8 | 1 | 24 | 0.8897214335 | 0.9130434783 | Henry Cohn, 2025 |
| 8 | 1 | 25 | 0.8891116857 | 0.9114583334 | Henry Cohn, 2025 |
| 8 | 1 | 26 | 0.8890483421 | 0.9100000000 | Henry Cohn, 2025 |
| 8 | 1 | 27 | 0.8890182115 | 0.9086538462 | Henry Cohn, 2025 |
| 8 | 1 | 28 | 0.8889403800 | 0.9074074075 | Henry Cohn, 2025 |
| 8 | 1 | 29 | 0.8888917489 | 0.9062500000 | Henry Cohn, 2025 |
| 8 | 1 | 30 | 0.8888888900 | 0.9051724138 | Henry Cohn, 2025 |
| 8 | 1 | 31 | 0.8888888888 | 0.9041666667 | |
| 8 | 1 | 32 | 0.8888888888 | 0.9032258065 | |
| 8 | 1 | 33 | 0.8752898806 | 0.9023437500 | |
| 8 | 1 | 34 | 0.8735966279 | 0.9015151516 | Henry Cohn, 2023 |
| 8 | 1 | 35 | 0.8724489795 | 0.9007352942 | |
| 8 | 1 | 36 | 0.8724489795 | 0.9000000000 | |
| 8 | 1 | 37 | 0.8570251735 | 0.8750000000 | |
| 8 | 1 | 38 | 0.8521149013 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 39 | 0.8490659200 | 0.8750000000 | |
| 8 | 1 | 40 | 0.8394839273 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 41 | 0.8336327072 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 42 | 0.8321803133 | 0.8750000000 | |
| 8 | 1 | 43 | 0.8252343912 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 44 | 0.8246210354 | 0.8750000000 | |
| 8 | 1 | 45 | 0.8180071672 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 46 | 0.8133111207 | 0.8750000000 | |
| 8 | 1 | 47 | 0.8099475483 | 0.8750000000 | |
| 8 | 1 | 48 | 0.8062414782 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 49 | 0.8006991244 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 50 | 0.7960527511 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 51 | 0.7915177625 | 0.8750000000 | Henry Cohn, 2025 |
| 8 | 1 | 52 | 0.7881086221 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 53 | 0.7874448256 | 0.8750000000 | |
| 8 | 1 | 54 | 0.7874469378 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 55 | 0.7782542157 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 56 | 0.7748346495 | 0.8750000000 | |
| 8 | 1 | 57 | 0.7726005037 | 0.8750000000 | |
| 8 | 1 | 58 | 0.7693598852 | 0.8750000000 | |
| 8 | 1 | 59 | 0.7665796417 | 0.8750000000 | Henry Cohn, 2024 |
| 8 | 1 | 60 | 0.7640649266 | 0.8750000000 | |
| 8 | 1 | 61 | 0.7614663919 | 0.8750000000 | |
| 8 | 1 | 62 | 0.7594322065 | 0.8750000000 | |
| 8 | 1 | 63 | 0.7572799338 | 0.8750000000 | |
| 8 | 1 | 64 | 0.7557164720 | 0.8750000000 | |
| 8 | 1 | 65 | 0.7542754622 | 0.8750000000 | |
| 8 | 1 | 66 | 0.7521498262 | 0.8750000000 | |
| 8 | 1 | 67 | 0.7509841150 | 0.8750000000 | |
| 8 | 1 | 68 | 0.7508437043 | 0.8750000000 | |
| 8 | 1 | 69 | 0.7505214729 | 0.8750000000 | |
| 8 | 1 | 70 | 0.7504163618 | 0.8750000000 | |
| 8 | 1 | 71 | 0.7504163618 | ||
| 8 | 1 | 72 | 0.7501027399 | ||
| 8 | 1 | 73 | 0.7500605860 | ||
| 8 | 1 | 74 | 0.7500546207 | ||
| 8 | 1 | 75 | 0.7500205088 | ||
| 8 | 1 | 76 | 0.7500001960 | ||
| 8 | 1 | 77 | 0.7499999999 | ||
| 8 | 1 | 78 | 0.7499999999 | ||
| 8 | 1 | 79 | 0.7499999999 | ||
| 8 | 1 | 80 | 0.7499999999 | ||
| 8 | 1 | 81 | 0.7499999999 | ||
| 8 | 1 | 82 | 0.7499999999 | ||
| 8 | 1 | 83 | 0.7499999999 | ||
| 8 | 1 | 84 | 0.7499999999 | ||
| 8 | 1 | 85 | 0.7499999999 | ||
| 8 | 1 | 86 | 0.7499999999 | ||
| 8 | 1 | 87 | 0.7499999999 | ||
| 8 | 1 | 88 | 0.7499999999 | ||
| 8 | 1 | 89 | 0.7499999999 | ||
| 8 | 1 | 90 | 0.7499999999 | ||
| 8 | 1 | 91 | 0.7499999999 | ||
| 8 | 1 | 92 | 0.7499999999 | ||
| 8 | 1 | 93 | 0.7499999999 | ||
| 8 | 1 | 94 | 0.7499999999 | ||
| 8 | 1 | 95 | 0.7499999999 | ||
| 8 | 1 | 96 | 0.7499999999 | ||
| 8 | 1 | 97 | 0.7499999999 | ||
| 8 | 1 | 98 | 0.7499999999 | ||
| 8 | 1 | 99 | 0.7499999999 | ||
| 8 | 1 | 100 | 0.7499999999 | ||
| 8 | 1 | 110 | 0.7499999999 | ||
| 8 | 1 | 120 | 0.7499999999 | ||
| ∗ 8 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 8 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound [4] |
| ∗ 8 | 2 | 5 | 1.8749999999 | 1.8750000000 | tight bound [4] |
| ∗ 8 | 2 | 6 | 1.7999999999 | 1.8000000000 | tight bound [4] |
| ∗ 8 | 2 | 7 | 1.7499999999 | 1.7500000000 | tight bound [4] |
| ∗ 8 | 2 | 8 | 1.7142857142 | 1.7142857143 | tight bound [5] |
| ∗ 8 | 2 | 9 | 1.6874999999 | 1.6875000000 | tight bound [4] |
| ∗ 8 | 2 | 10 | 1.6666666666 | 1.6666666667 | tight bound [4] |
| ∗ 8 | 2 | 11 | 1.6499999999 | 1.6500000000 | tight bound [4] |
| ∗ 8 | 2 | 12 | 1.6363636363 | 1.6363636364 | tight bound [4] |
| ∗ 8 | 2 | 13 | 1.6249999999 | 1.6250000000 | tight bound [4] |
| ∗ 8 | 2 | 14 | 1.6153846153 | 1.6153846154 | tight bound [4] |
| ∗ 8 | 2 | 15 | 1.6071428571 | 1.6071428572 | tight bound [4] |
| ∗ 8 | 2 | 16 | 1.5999999999 | 1.6000000000 | tight bound [4] |
| ∗ 8 | 2 | 17 | 1.5937499999 | 1.5937500000 | tight bound [4] |
| ∗ 8 | 2 | 18 | 1.5882352941 | 1.5882352942 | tight bound [4] |
| ∗ 8 | 2 | 19 | 1.5833333333 | 1.5833333334 | tight bound [4] |
| ∗ 8 | 2 | 20 | 1.5789473684 | 1.5789473685 | tight bound [1] |
| ∗ 8 | 2 | 21 | 1.5749999999 | 1.5750000000 | tight bound [4] |
| 8 | 2 | 22 | 1.5714206524 | 1.5714285715 | |
| 8 | 2 | 23 | 1.5679718798 | 1.5681818182 | |
| 8 | 2 | 24 | 1.5638956526 | 1.5652173914 | |
| 8 | 2 | 25 | 1.5594411386 | 1.5625000000 | |
| 8 | 2 | 26 | 1.5556048492 | 1.5600000000 | |
| 8 | 2 | 27 | 1.5555555555 | 1.5576923077 | |
| ∗ 8 | 2 | 28 | 1.5555555555 | 1.5555555556 | tight bound [5] |
| 8 | 2 | 29 | 1.5455014556 | 1.5535714286 | |
| 8 | 2 | 30 | 1.5397623054 | 1.5517241380 | |
| 8 | 2 | 31 | 1.5342474644 | 1.5500000000 | |
| 8 | 2 | 32 | 1.5304211816 | 1.5483870968 | |
| 8 | 2 | 33 | 1.5244179223 | 1.5468750000 | |
| 8 | 2 | 34 | 1.5216400745 | 1.5454545455 | |
| 8 | 2 | 35 | 1.5157682671 | 1.5441176471 | |
| 8 | 2 | 36 | 1.5096992398 | 1.5428571429 | |
| ∗ 8 | 2 | 37 | 1.4999999999 | 1.5000000000 | tight bound [1] |
| ∗ 8 | 2 | 38 | 1.4999999999 | 1.5000000000 | tight bound [1] |
| ∗ 8 | 2 | 39 | 1.4999999999 | 1.5000000000 | tight bound [1] |
| ∗ 8 | 2 | 40 | 1.4999999999 | 1.5000000000 | tight bound [1] |
| ∗ 8 | 2 | 41 | 1.4999999999 | 1.5000000000 | |
| ∗ 8 | 2 | 42 | 1.4999999999 | 1.5000000000 | |
| ∗ 8 | 2 | 43 | 1.4999999999 | 1.5000000000 | |
| ∗ 8 | 2 | 44 | 1.4999999999 | 1.5000000000 | |
| 8 | 2 | 45 | 1.4839496628 | 1.5000000000 | |
| 8 | 2 | 46 | 1.4820747225 | 1.5000000000 | |
| 8 | 2 | 47 | 1.4574747629 | 1.5000000000 | |
| 8 | 2 | 48 | 1.4493472456 | 1.5000000000 | |
| 8 | 2 | 49 | 1.4430613703 | 1.5000000000 | |
| 8 | 2 | 50 | 1.4370120052 | 1.5000000000 | |
| 8 | 2 | 51 | 1.4295527808 | 1.5000000000 | |
| 8 | 2 | 52 | 1.4250488712 | 1.5000000000 | |
| 8 | 2 | 53 | 1.4205582396 | 1.5000000000 | |
| 8 | 2 | 54 | 1.4169261433 | 1.5000000000 | |
| 8 | 2 | 55 | 1.4139410635 | 1.5000000000 | |
| 8 | 2 | 56 | 1.4103001046 | 1.5000000000 | |
| 8 | 2 | 57 | 1.4067766082 | 1.5000000000 | |
| 8 | 2 | 58 | 1.4035135119 | 1.5000000000 | |
| 8 | 2 | 59 | 1.4005185580 | 1.5000000000 | |
| 8 | 2 | 60 | 1.3970521508 | 1.5000000000 | |
| 8 | 2 | 61 | 1.3938797321 | 1.5000000000 | |
| 8 | 2 | 62 | 1.3917492871 | 1.5000000000 | |
| 8 | 2 | 63 | 1.3902410899 | 1.5000000000 | |
| 8 | 2 | 64 | 1.3855696923 | 1.5000000000 | |
| 8 | 2 | 65 | 1.3830155332 | 1.5000000000 | |
| 8 | 2 | 66 | 1.3798282875 | 1.5000000000 | |
| 8 | 2 | 67 | 1.3780390030 | 1.5000000000 | |
| 8 | 2 | 68 | 1.3747839937 | 1.5000000000 | |
| 8 | 2 | 69 | 1.3720023674 | 1.5000000000 | |
| 8 | 2 | 70 | 1.3700365322 | 1.5000000000 | |
| 8 | 2 | 71 | 1.3669202189 | ||
| 8 | 2 | 72 | 1.3648267211 | ||
| 8 | 2 | 73 | 1.3623325496 | ||
| 8 | 2 | 74 | 1.3601012069 | ||
| 8 | 2 | 75 | 1.3580251593 | ||
| 8 | 2 | 76 | 1.3555540286 | ||
| 8 | 2 | 77 | 1.3530842002 | ||
| 8 | 2 | 78 | 1.3510414503 | ||
| 8 | 2 | 79 | 1.3491322329 | ||
| 8 | 2 | 80 | 1.3471137141 | ||
| 8 | 2 | 81 | 1.3449341769 | ||
| 8 | 2 | 82 | 1.3428427590 | ||
| 8 | 2 | 83 | 1.3410774953 | ||
| 8 | 2 | 84 | 1.3390354010 | ||
| 8 | 2 | 85 | 1.3372699138 | ||
| 8 | 2 | 86 | 1.3353916412 | ||
| 8 | 2 | 87 | 1.3334073764 | ||
| 8 | 2 | 88 | 1.3317243306 | ||
| 8 | 2 | 89 | 1.3298350519 | ||
| 8 | 2 | 90 | 1.3282466826 | ||
| 8 | 2 | 91 | 1.3265256855 | ||
| 8 | 2 | 92 | 1.3246678207 | ||
| 8 | 2 | 93 | 1.3229906401 | ||
| 8 | 2 | 94 | 1.3214178545 | ||
| 8 | 2 | 95 | 1.3198705486 | ||
| 8 | 2 | 96 | 1.3182364199 | ||
| 8 | 2 | 97 | 1.3167432522 | ||
| 8 | 2 | 98 | 1.3150944772 | ||
| 8 | 2 | 99 | 1.3135775953 | ||
| 8 | 2 | 100 | 1.3123160347 | ||
| 8 | 3 | 3 | 2.7499999999 | 2.8125000000 | |
| ∗ 8 | 3 | 4 | 2.4999999999 | 2.5000000000 | tight bound [4] |
| ∗ 8 | 3 | 5 | 2.3437499999 | 2.3437500000 | tight bound [4] |
| ∗ 8 | 3 | 6 | 2.2499999999 | 2.2500000000 | tight bound [4] |
| ∗ 8 | 3 | 7 | 2.1874999999 | 2.1875000000 | tight bound [4] |
| ∗ 8 | 3 | 8 | 2.1428571428 | 2.1428571429 | tight bound [4] |
| ∗ 8 | 3 | 9 | 2.1093749999 | 2.1093750000 | tight bound [4] |
| ∗ 8 | 3 | 10 | 2.0833333333 | 2.0833333334 | tight bound [4] |
| ∗ 8 | 3 | 11 | 2.0624999999 | 2.0625000000 | tight bound [4] |
| ∗ 8 | 3 | 12 | 2.0454545454 | 2.0454545455 | tight bound [4] |
| ∗ 8 | 3 | 13 | 2.0312499999 | 2.0312500000 | tight bound [4] |
| ∗ 8 | 3 | 14 | 2.0192307692 | 2.0192307693 | tight bound [4] |
| ∗ 8 | 3 | 15 | 2.0089285714 | 2.0089285715 | tight bound [4] |
| ∗ 8 | 3 | 16 | 1.9999999999 | 2.0000000000 | tight bound [4] |
| ∗ 8 | 3 | 17 | 1.9921874999 | 1.9921875000 | tight bound [4] |
| ∗ 8 | 3 | 18 | 1.9852941176 | 1.9852941177 | tight bound [4] |
| ∗ 8 | 3 | 19 | 1.9791666666 | 1.9791666667 | tight bound [4] |
| ∗ 8 | 3 | 20 | 1.9736842105 | 1.9736842106 | tight bound [4] |
| ∗ 8 | 3 | 21 | 1.9687499999 | 1.9687500000 | tight bound [4] |
| ∗ 8 | 3 | 22 | 1.9642857142 | 1.9642857143 | tight bound [4] |
| ∗ 8 | 3 | 23 | 1.9602272727 | 1.9602272728 | tight bound [4] |
| ∗ 8 | 3 | 24 | 1.9565217391 | 1.9565217392 | tight bound [4] |
| ∗ 8 | 3 | 25 | 1.9531249999 | 1.9531250000 | tight bound [4] |
| ∗ 8 | 3 | 26 | 1.9499999999 | 1.9500000000 | tight bound [4] |
| ∗ 8 | 3 | 27 | 1.9471153846 | 1.9471153847 | tight bound [4] |
| ∗ 8 | 3 | 28 | 1.9444444444 | 1.9444444445 | tight bound [4] |
| 8 | 3 | 29 | 1.9419607487 | 1.9419642858 | |
| 8 | 3 | 30 | 1.9393067306 | 1.9396551725 | |
| 8 | 3 | 31 | 1.9364104091 | 1.9375000000 | |
| 8 | 3 | 32 | 1.9331940793 | 1.9354838710 | |
| 8 | 3 | 33 | 1.9302953436 | 1.9335937500 | |
| 8 | 3 | 34 | 1.9269015115 | 1.9318181819 | |
| 8 | 3 | 35 | 1.9242740105 | 1.9301470589 | |
| 8 | 3 | 36 | 1.9215462348 | 1.9285714286 | |
| ∗ 8 | 3 | 37 | 1.8749999999 | 1.8750000000 | |
| ∗ 8 | 3 | 38 | 1.8749999999 | 1.8750000000 | |
| ∗ 8 | 3 | 39 | 1.8749999999 | 1.8750000000 | |
| 8 | 3 | 40 | 1.8726311782 | 1.8750000000 | |
| 8 | 3 | 41 | 1.8695466764 | 1.8750000000 | |
| 8 | 3 | 42 | 1.8672191190 | 1.8750000000 | |
| 8 | 3 | 43 | 1.8617025339 | 1.8750000000 | |
| 8 | 3 | 44 | 1.8573529204 | 1.8750000000 | |
| 8 | 3 | 45 | 1.8523703681 | 1.8750000000 | |
| 8 | 3 | 46 | 1.8481658553 | 1.8750000000 | |
| 8 | 3 | 47 | 1.8439643508 | 1.8750000000 | |
| 8 | 3 | 48 | 1.8389582224 | 1.8750000000 | |
| 8 | 3 | 49 | 1.8376213980 | 1.8750000000 | |
| 8 | 3 | 50 | 1.8312093923 | 1.8750000000 | |
| 8 | 3 | 51 | 1.8275803295 | 1.8750000000 | |
| 8 | 3 | 52 | 1.8241292396 | 1.8750000000 | |
| 8 | 3 | 53 | 1.8185356544 | 1.8750000000 | |
| 8 | 3 | 54 | 1.8144700115 | 1.8750000000 | |
| 8 | 3 | 55 | 1.8101807807 | 1.8750000000 | |
| 8 | 3 | 56 | 1.8075235832 | 1.8750000000 | |
| 8 | 3 | 57 | 1.8033602301 | 1.8750000000 | |
| 8 | 3 | 58 | 1.8002016308 | 1.8750000000 | |
| 8 | 3 | 59 | 1.7964451724 | 1.8750000000 | |
| 8 | 3 | 60 | 1.7935832562 | 1.8750000000 | |
| 8 | 3 | 61 | 1.7910813085 | 1.8750000000 | |
| 8 | 3 | 62 | 1.7875667870 | 1.8750000000 | |
| 8 | 3 | 63 | 1.7850015275 | 1.8750000000 | |
| 8 | 3 | 64 | 1.7823409012 | 1.8750000000 | |
| 8 | 3 | 65 | 1.7790680369 | 1.8750000000 | |
| 8 | 3 | 66 | 1.7762541407 | 1.8750000000 | |
| 8 | 3 | 67 | 1.7738706343 | 1.8750000000 | |
| 8 | 3 | 68 | 1.7707761794 | 1.8750000000 | |
| 8 | 3 | 69 | 1.7684878328 | 1.8750000000 | |
| 8 | 3 | 70 | 1.7671559957 | 1.8750000000 | |
| 8 | 3 | 71 | 1.7628283567 | ||
| 8 | 3 | 72 | 1.7602025129 | ||
| 8 | 3 | 73 | 1.7582301602 | ||
| 8 | 3 | 74 | 1.7554788480 | ||
| 8 | 3 | 75 | 1.7533820090 | ||
| 8 | 3 | 76 | 1.7509328315 | ||
| 8 | 3 | 77 | 1.7499651223 | ||
| 8 | 3 | 78 | 1.7456354580 | ||
| 8 | 3 | 79 | 1.7439917163 | ||
| 8 | 3 | 80 | 1.7414874399 | ||
| 8 | 3 | 81 | 1.7391374780 | ||
| 8 | 3 | 82 | 1.7372080072 | ||
| 8 | 3 | 83 | 1.7350507124 | ||
| 8 | 3 | 84 | 1.7340896616 | ||
| 8 | 3 | 85 | 1.7306136825 | ||
| 8 | 3 | 86 | 1.7282004008 | ||
| 8 | 3 | 87 | 1.7264150137 | ||
| 8 | 3 | 88 | 1.7238915044 | ||
| 8 | 3 | 89 | 1.7220491958 | ||
| 8 | 3 | 90 | 1.7197432344 | ||
| 8 | 3 | 91 | 1.7183757672 | ||
| 8 | 3 | 92 | 1.7156619328 | ||
| 8 | 3 | 93 | 1.7136166168 | ||
| 8 | 3 | 94 | 1.7114385813 | ||
| 8 | 3 | 95 | 1.7099987261 | ||
| 8 | 3 | 96 | 1.7074738729 | ||
| 8 | 3 | 97 | 1.7055539271 | ||
| 8 | 3 | 98 | 1.7036747377 | ||
| 8 | 3 | 99 | 1.7017539456 | ||
| 8 | 3 | 100 | 1.6995717891 | ||
| ∗ 8 | 4 | 7 | 2.3333333333 | 2.3333333334 | tight bound [4] |
| ∗ 8 | 4 | 8 | 2.2857142857 | 2.2857142858 | tight bound [4] |
| ∗ 8 | 4 | 9 | 2.2499999999 | 2.2500000000 | tight bound [4] |
| ∗ 8 | 4 | 10 | 2.2222222222 | 2.2222222223 | tight bound [4] |
| ∗ 8 | 4 | 12 | 2.1818181818 | 2.1818181819 | tight bound [4] |
| ∗ 8 | 4 | 14 | 2.1538461538 | 2.1538461539 | tight bound [4] |
| ∗ 8 | 4 | 15 | 2.1428571428 | 2.1428571429 | tight bound [4] |
| ∗ 8 | 4 | 16 | 2.1333333333 | 2.1333333334 | tight bound [4] |
| ∗ 8 | 4 | 17 | 2.1249999999 | 2.1250000000 | tight bound [4] |
| ∗ 8 | 4 | 18 | 2.1176470588 | 2.1176470589 | tight bound [4] |
| ∗ 8 | 4 | 21 | 2.0999999999 | 2.1000000000 | tight bound [4] |
| ∗ 8 | 4 | 22 | 2.0952380952 | 2.0952380953 | tight bound [4] |
| ∗ 8 | 4 | 24 | 2.0869565217 | 2.0869565218 | tight bound [4] |
| ∗ 8 | 4 | 25 | 2.0833333333 | 2.0833333334 | tight bound [4] |
| ∗ 8 | 4 | 26 | 2.0799999999 | 2.0800000000 | tight bound [4] |
| ∗ 8 | 4 | 28 | 2.0740740740 | 2.0740740741 | tight bound [4] |
| ∗ 8 | 4 | 29 | 2.0714285714 | 2.0714285715 | tight bound [4] |
| ∗ 8 | 4 | 30 | 2.0689655172 | 2.0689655173 | tight bound [4] |
| 8 | 4 | 31 | 2.0666645769 | 2.0666666667 | |
| 8 | 4 | 32 | 2.0639741004 | 2.0645161291 | |
| 8 | 4 | 33 | 2.0608076723 | 2.0625000000 | |
| 8 | 4 | 34 | 2.0577850550 | 2.0606060607 | |
| 8 | 4 | 35 | 2.0554845926 | 2.0588235295 | |
| 8 | 4 | 36 | 2.0537386119 | 2.0571428572 | |
| ∗ 8 | 4 | 37 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 40 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 41 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 42 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 43 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 48 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 51 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 52 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 53 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 54 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 55 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 56 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 57 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 58 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 59 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 60 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 61 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 62 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 63 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 64 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 65 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 66 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 67 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 68 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 69 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| ∗ 8 | 4 | 70 | 2.0000000000 | 2.0000000000 | tight bound [5] |
| 8 | 4 | 71 | 1.9433029277 | ||
| 8 | 4 | 72 | 1.9400233117 | ||
| 8 | 4 | 73 | 1.9170010845 | ||
| 8 | 4 | 74 | 1.9129187037 | ||
| 8 | 4 | 75 | 1.8989251363 | ||
| 8 | 4 | 76 | 1.8946920214 | ||
| 8 | 4 | 77 | 1.8859485889 | ||
| 8 | 4 | 78 | 1.8814156932 | ||
| 8 | 4 | 79 | 1.8750405183 | ||
| 8 | 4 | 80 | 1.8709569658 | ||
| 8 | 4 | 81 | 1.8662955667 | ||
| 8 | 4 | 82 | 1.8625465870 | ||
| 8 | 4 | 83 | 1.8589471846 | ||
| 8 | 4 | 84 | 1.8569358472 | ||
| 8 | 4 | 85 | 1.8527867380 | ||
| 8 | 4 | 86 | 1.8499817093 | ||
| 8 | 4 | 87 | 1.8472734989 | ||
| 8 | 4 | 88 | 1.8443317622 | ||
| 8 | 4 | 89 | 1.8417887120 | ||
| 8 | 4 | 90 | 1.8396810530 | ||
| 8 | 4 | 91 | 1.8395554785 | ||
| 8 | 4 | 92 | 1.8351483298 | ||
| 8 | 4 | 93 | 1.8334809404 | ||
| 8 | 4 | 94 | 1.8310471183 | ||
| 8 | 4 | 95 | 1.8297475483 | ||
| 8 | 4 | 96 | 1.8275481590 | ||
| 8 | 4 | 97 | 1.8258608290 | ||
| 8 | 4 | 98 | 1.8241569036 | ||
| 8 | 4 | 99 | 1.8219411153 | ||
| 8 | 4 | 100 | 1.8195715222 | ||
| ∗ 9 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 9 | 1 | 10 | 0.9876543209 | 0.9876543210 | tight bound |
| 9 | 1 | 11 | 0.9734393342 | 0.9777777778 | |
| 9 | 1 | 12 | 0.9666046313 | 0.9696969697 | |
| 9 | 1 | 13 | 0.9563707159 | 0.9629629630 | Henry Cohn [2] |
| 9 | 1 | 14 | 0.9512036178 | 0.9572649573 | |
| 9 | 1 | 15 | 0.9455684462 | 0.9523809524 | Henry Cohn [2] |
| 9 | 1 | 16 | 0.9411764705 | 0.9481481482 | |
| 9 | 1 | 17 | 0.9411764705 | 0.9444444445 | |
| ∗ 9 | 1 | 18 | 0.9411764705 | 0.9411764706 | tight bound |
| 9 | 1 | 19 | 0.9283489889 | 0.9382716050 | Henry Cohn, 2025 |
| 9 | 1 | 20 | 0.9261177246 | 0.9356725147 | |
| 9 | 1 | 21 | 0.9217122601 | 0.9333333334 | |
| 9 | 1 | 22 | 0.9163582686 | 0.9312169313 | |
| 9 | 1 | 23 | 0.9120511821 | 0.9292929293 | |
| 9 | 1 | 24 | 0.9111188873 | 0.9275362319 | |
| 9 | 1 | 25 | 0.9076889007 | 0.9259259260 | |
| 9 | 1 | 26 | 0.9064850358 | 0.9244444445 | Henry Cohn, 2025 |
| 9 | 1 | 27 | 0.9010440904 | 0.9230769231 | Henry Cohn, 2024 |
| 9 | 1 | 28 | 0.9001504304 | 0.9218106996 | |
| 9 | 1 | 29 | 0.8995011921 | 0.9206349207 | |
| 9 | 1 | 30 | 0.8995011921 | 0.9195402299 | |
| 9 | 1 | 31 | 0.8923971992 | 0.9185185186 | Henry Cohn, 2025 |
| 9 | 1 | 32 | 0.8912357215 | 0.9175627241 | Henry Cohn, 2024 |
| 9 | 1 | 33 | 0.8907154439 | 0.9166666667 | Henry Cohn, 2025 |
| 9 | 1 | 34 | 0.8902294979 | 0.9158249159 | Henry Cohn, 2025 |
| 9 | 1 | 35 | 0.8900381448 | 0.9150326798 | Henry Cohn, 2024 |
| 9 | 1 | 36 | 0.8895205541 | 0.9142857143 | Henry Cohn, 2025 |
| 9 | 1 | 37 | 0.8893353783 | 0.9135802470 | Henry Cohn, 2024 |
| 9 | 1 | 38 | 0.8891997707 | 0.9129129130 | Henry Cohn, 2024 |
| 9 | 1 | 39 | 0.8891005773 | 0.9122807018 | Henry Cohn, 2023 |
| 9 | 1 | 40 | 0.8888888888 | 0.9116809117 | |
| 9 | 1 | 41 | 0.8888888888 | 0.9111111112 | |
| 9 | 1 | 42 | 0.8888888888 | 0.9105691057 | |
| 9 | 1 | 43 | 0.8888888888 | 0.9100529101 | |
| 9 | 1 | 44 | 0.8888888888 | 0.9095607236 | |
| 9 | 1 | 45 | 0.8888888888 | 0.9090909091 | |
| ∗ 9 | 1 | 46 | 0.8888888888 | 0.8888888889 | tight bound |
| ∗ 9 | 1 | 47 | 0.8888888888 | 0.8888888889 | tight bound |
| ∗ 9 | 1 | 48 | 0.8888888888 | 0.8888888889 | tight bound |
| 9 | 1 | 49 | 0.8603426108 | 0.8888888889 | Henry Cohn, 2025 |
| 9 | 1 | 50 | 0.8565348344 | 0.8888888889 | Henry Cohn, 2024 |
| 9 | 1 | 51 | 0.8474254505 | 0.8888888889 | |
| 9 | 1 | 52 | 0.8448475070 | 0.8888888889 | |
| 9 | 1 | 53 | 0.8414466076 | 0.8888888889 | |
| 9 | 1 | 54 | 0.8389983203 | 0.8888888889 | |
| 9 | 1 | 55 | 0.8339800666 | 0.8888888889 | |
| 9 | 1 | 56 | 0.8299733389 | 0.8888888889 | Henry Cohn, 2025 |
| 9 | 1 | 57 | 0.8265301532 | 0.8888888889 | |
| 9 | 1 | 58 | 0.8245101220 | 0.8888888889 | |
| 9 | 1 | 59 | 0.8211964302 | 0.8888888889 | |
| 9 | 1 | 60 | 0.8188657535 | 0.8888888889 | |
| 9 | 1 | 61 | 0.8156219469 | 0.8888888889 | |
| 9 | 1 | 62 | 0.8131485938 | 0.8888888889 | |
| 9 | 1 | 63 | 0.8101339005 | 0.8888888889 | |
| 9 | 1 | 64 | 0.8077509620 | 0.8888888889 | |
| 9 | 1 | 65 | 0.8049939458 | 0.8888888889 | |
| 9 | 1 | 66 | 0.8020688238 | 0.8888888889 | |
| 9 | 1 | 67 | 0.7996575222 | 0.8888888889 | |
| 9 | 1 | 68 | 0.7971631370 | 0.8888888889 | |
| 9 | 1 | 69 | 0.7942599128 | 0.8888888889 | |
| 9 | 1 | 70 | 0.7923016940 | 0.8888888889 | |
| 9 | 1 | 71 | 0.7897734473 | 0.8888888889 | |
| 9 | 1 | 72 | 0.7876276159 | 0.8888888889 | |
| 9 | 1 | 73 | 0.7852787663 | 0.8888888889 | |
| 9 | 1 | 74 | 0.7831714927 | 0.8888888889 | |
| 9 | 1 | 75 | 0.7811886697 | 0.8888888889 | |
| 9 | 1 | 76 | 0.7793323357 | 0.8888888889 | |
| 9 | 1 | 77 | 0.7769543627 | 0.8888888889 | |
| 9 | 1 | 78 | 0.7752313552 | 0.8888888889 | |
| 9 | 1 | 79 | 0.7734929304 | 0.8888888889 | |
| 9 | 1 | 80 | 0.7718407051 | 0.8888888889 | |
| 9 | 1 | 81 | 0.7702618281 | 0.8888888889 | |
| 9 | 1 | 82 | 0.7683614943 | 0.8888888889 | |
| 9 | 1 | 83 | 0.7668828817 | 0.8888888889 | |
| 9 | 1 | 84 | 0.7650876664 | 0.8888888889 | |
| 9 | 1 | 85 | 0.7633192720 | 0.8888888889 | |
| 9 | 1 | 86 | 0.7625818132 | 0.8888888889 | |
| 9 | 1 | 87 | 0.7607612858 | 0.8888888889 | |
| 9 | 1 | 88 | 0.7590444251 | 0.8888888889 | |
| 9 | 1 | 89 | 0.7578723853 | ||
| 9 | 1 | 90 | 0.7561756538 | ||
| 9 | 1 | 91 | 0.7553129850 | ||
| 9 | 1 | 92 | 0.7540368321 | ||
| 9 | 1 | 93 | 0.7532285242 | ||
| 9 | 1 | 94 | 0.7511539729 | ||
| 9 | 1 | 95 | 0.7510180315 | ||
| 9 | 1 | 96 | 0.7507511058 | ||
| 9 | 1 | 97 | 0.7503713808 | ||
| 9 | 1 | 98 | 0.7503713808 | ||
| 9 | 1 | 99 | 0.7503713808 | ||
| 9 | 1 | 100 | 0.7503713808 | ||
| ∗ 9 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 9 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| 9 | 2 | 5 | 1.9374999999 | 1.9444444445 | |
| ∗ 9 | 2 | 6 | 1.8666666666 | 1.8666666667 | |
| ∗ 9 | 2 | 7 | 1.8148148148 | 1.8148148149 | |
| ∗ 9 | 2 | 8 | 1.7777777777 | 1.7777777778 | |
| ∗ 9 | 2 | 9 | 1.7499999999 | 1.7500000000 | |
| ∗ 9 | 2 | 10 | 1.7283950617 | 1.7283950618 | |
| ∗ 9 | 2 | 11 | 1.7111111111 | 1.7111111112 | |
| ∗ 9 | 2 | 12 | 1.6969696969 | 1.6969696970 | |
| ∗ 9 | 2 | 13 | 1.6851851851 | 1.6851851852 | |
| ∗ 9 | 2 | 14 | 1.6752136752 | 1.6752136753 | |
| ∗ 9 | 2 | 15 | 1.6666666666 | 1.6666666667 | |
| ∗ 9 | 2 | 16 | 1.6592592592 | 1.6592592593 | |
| ∗ 9 | 2 | 17 | 1.6527777777 | 1.6527777778 | |
| ∗ 9 | 2 | 18 | 1.6470588235 | 1.6470588236 | |
| ∗ 9 | 2 | 19 | 1.6419753086 | 1.6419753087 | |
| ∗ 9 | 2 | 20 | 1.6374269005 | 1.6374269006 | |
| ∗ 9 | 2 | 21 | 1.6333333333 | 1.6333333334 | |
| ∗ 9 | 2 | 22 | 1.6296296296 | 1.6296296297 | |
| ∗ 9 | 2 | 23 | 1.6262626262 | 1.6262626263 | |
| ∗ 9 | 2 | 24 | 1.6231884057 | 1.6231884058 | |
| 9 | 2 | 25 | 1.6203699489 | 1.6203703704 | |
| 9 | 2 | 26 | 1.6177255610 | 1.6177777778 | |
| 9 | 2 | 27 | 1.6153819649 | 1.6153846154 | |
| 9 | 2 | 28 | 1.6118366588 | 1.6131687243 | |
| 9 | 2 | 29 | 1.6082669755 | 1.6111111112 | |
| 9 | 2 | 30 | 1.6048835870 | 1.6091954023 | |
| 9 | 2 | 31 | 1.6011163926 | 1.6074074075 | |
| 9 | 2 | 32 | 1.5977899577 | 1.6057347671 | |
| 9 | 2 | 33 | 1.5935274222 | 1.6041666667 | |
| 9 | 2 | 34 | 1.5911040659 | 1.6026936027 | |
| 9 | 2 | 35 | 1.5892944715 | 1.6013071896 | |
| 9 | 2 | 36 | 1.5885376440 | 1.6000000000 | |
| 9 | 2 | 37 | 1.5815973868 | 1.5987654321 | |
| 9 | 2 | 38 | 1.5768416943 | 1.5975975976 | |
| 9 | 2 | 39 | 1.5729713339 | 1.5964912281 | |
| 9 | 2 | 40 | 1.5697254467 | 1.5954415955 | |
| 9 | 2 | 41 | 1.5664722480 | 1.5944444445 | |
| 9 | 2 | 42 | 1.5639384346 | 1.5934959350 | |
| 9 | 2 | 43 | 1.5615970638 | 1.5925925926 | |
| 9 | 2 | 44 | 1.5587900803 | 1.5917312662 | |
| 9 | 2 | 45 | 1.5569956637 | 1.5909090910 | |
| 9 | 2 | 46 | 1.5484749960 | 1.5555555556 | |
| 9 | 2 | 47 | 1.5412989077 | 1.5555555556 | |
| 9 | 2 | 48 | 1.5353118322 | 1.5555555556 | |
| 9 | 2 | 49 | 1.5304977746 | 1.5555555556 | |
| 9 | 2 | 50 | 1.5258308162 | 1.5555555556 | |
| 9 | 2 | 51 | 1.5206497331 | 1.5555555556 | |
| 9 | 2 | 52 | 1.5164710013 | 1.5555555556 | |
| 9 | 2 | 53 | 1.5131295727 | 1.5555555556 | |
| 9 | 2 | 54 | 1.5105181411 | 1.5555555556 | |
| 9 | 2 | 55 | 1.5067144215 | 1.5555555556 | |
| 9 | 2 | 56 | 1.5037005939 | 1.5555555556 | |
| 9 | 2 | 57 | 1.4999780657 | 1.5555555556 | |
| 9 | 2 | 58 | 1.4968868489 | 1.5555555556 | |
| 9 | 2 | 59 | 1.4936256041 | 1.5555555556 | |
| 9 | 2 | 60 | 1.4909153761 | 1.5555555556 | |
| 9 | 2 | 61 | 1.4875648570 | 1.5555555556 | |
| 9 | 2 | 62 | 1.4850871226 | 1.5555555556 | |
| 9 | 2 | 63 | 1.4821140690 | 1.5555555556 | |
| 9 | 2 | 64 | 1.4792446925 | 1.5555555556 | |
| 9 | 2 | 65 | 1.4766507050 | 1.5555555556 | |
| 9 | 2 | 66 | 1.4740711478 | 1.5555555556 | |
| 9 | 2 | 67 | 1.4716929417 | 1.5555555556 | |
| 9 | 2 | 68 | 1.4685202501 | 1.5555555556 | |
| 9 | 2 | 69 | 1.4659600414 | 1.5555555556 | |
| 9 | 2 | 70 | 1.4637968014 | 1.5555555556 | |
| 9 | 2 | 71 | 1.4611697031 | 1.5555555556 | |
| 9 | 2 | 72 | 1.4600879581 | 1.5555555556 | |
| 9 | 2 | 73 | 1.4566522535 | 1.5555555556 | |
| 9 | 2 | 74 | 1.4542258648 | 1.5555555556 | |
| 9 | 2 | 75 | 1.4521441992 | 1.5555555556 | |
| 9 | 2 | 76 | 1.4496867965 | 1.5555555556 | |
| 9 | 2 | 77 | 1.4474868301 | 1.5555555556 | |
| 9 | 2 | 78 | 1.4456031808 | 1.5555555556 | |
| 9 | 2 | 79 | 1.4435490050 | 1.5555555556 | |
| 9 | 2 | 80 | 1.4414773944 | 1.5555555556 | |
| 9 | 2 | 81 | 1.4390785389 | 1.5555555556 | |
| 9 | 2 | 82 | 1.4373773045 | 1.5555555556 | |
| 9 | 2 | 83 | 1.4353263127 | 1.5555555556 | |
| 9 | 2 | 84 | 1.4333863684 | 1.5555555556 | |
| 9 | 2 | 85 | 1.4312604068 | 1.5555555556 | |
| 9 | 2 | 86 | 1.4291855679 | 1.5555555556 | |
| 9 | 2 | 87 | 1.4274275860 | 1.5555555556 | |
| 9 | 2 | 88 | 1.4257349588 | 1.5555555556 | |
| 9 | 2 | 89 | 1.4238650794 | ||
| 9 | 2 | 90 | 1.4220800143 | ||
| 9 | 2 | 91 | 1.4203214018 | ||
| 9 | 2 | 92 | 1.4187042418 | ||
| 9 | 2 | 93 | 1.4166937540 | ||
| 9 | 2 | 94 | 1.4151096472 | ||
| 9 | 2 | 95 | 1.4133764335 | ||
| 9 | 2 | 96 | 1.4117408691 | ||
| 9 | 2 | 97 | 1.4101931504 | ||
| 9 | 2 | 98 | 1.4084149672 | ||
| 9 | 2 | 99 | 1.4072462533 | ||
| 9 | 2 | 100 | 1.4051137347 | ||
| ∗ 9 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 9 | 3 | 4 | 2.6666666666 | 2.6666666667 | |
| ∗ 9 | 3 | 5 | 2.4999999999 | 2.5000000000 | |
| ∗ 9 | 3 | 6 | 2.3999999999 | 2.4000000000 | |
| ∗ 9 | 3 | 7 | 2.3333333333 | 2.3333333334 | |
| ∗ 9 | 3 | 8 | 2.2857142857 | 2.2857142858 | |
| ∗ 9 | 3 | 9 | 2.2499999999 | 2.2500000000 | |
| ∗ 9 | 3 | 10 | 2.2222222222 | 2.2222222223 | |
| ∗ 9 | 3 | 11 | 2.1999999999 | 2.2000000000 | |
| ∗ 9 | 3 | 12 | 2.1818181818 | 2.1818181819 | |
| ∗ 9 | 3 | 13 | 2.1666666666 | 2.1666666667 | |
| ∗ 9 | 3 | 14 | 2.1538461538 | 2.1538461539 | |
| ∗ 9 | 3 | 15 | 2.1428571428 | 2.1428571429 | |
| ∗ 9 | 3 | 16 | 2.1333333333 | 2.1333333334 | |
| ∗ 9 | 3 | 17 | 2.1249999999 | 2.1250000000 | |
| ∗ 9 | 3 | 18 | 2.1176470588 | 2.1176470589 | |
| ∗ 9 | 3 | 19 | 2.1111111111 | 2.1111111112 | |
| ∗ 9 | 3 | 20 | 2.1052631578 | 2.1052631579 | |
| ∗ 9 | 3 | 21 | 2.0999999999 | 2.1000000000 | |
| ∗ 9 | 3 | 22 | 2.0952380952 | 2.0952380953 | |
| ∗ 9 | 3 | 23 | 2.0909090909 | 2.0909090910 | |
| ∗ 9 | 3 | 24 | 2.0869565217 | 2.0869565218 | |
| ∗ 9 | 3 | 25 | 2.0833333333 | 2.0833333334 | |
| ∗ 9 | 3 | 26 | 2.0799999999 | 2.0800000000 | |
| ∗ 9 | 3 | 27 | 2.0769230769 | 2.0769230770 | |
| ∗ 9 | 3 | 28 | 2.0740740740 | 2.0740740741 | |
| ∗ 9 | 3 | 29 | 2.0714285714 | 2.0714285715 | |
| ∗ 9 | 3 | 30 | 2.0689655172 | 2.0689655173 | |
| ∗ 9 | 3 | 31 | 2.0666666666 | 2.0666666667 | |
| ∗ 9 | 3 | 32 | 2.0645161290 | 2.0645161291 | |
| ∗ 9 | 3 | 33 | 2.0624999999 | 2.0625000000 | |
| ∗ 9 | 3 | 34 | 2.0606060606 | 2.0606060607 | |
| 9 | 3 | 35 | 2.0587809882 | 2.0588235295 | |
| 9 | 3 | 36 | 2.0570954026 | 2.0571428572 | |
| 9 | 3 | 37 | 2.0544029639 | 2.0555555556 | |
| 9 | 3 | 38 | 2.0519649279 | 2.0540540541 | |
| 9 | 3 | 39 | 2.0494456271 | 2.0526315790 | |
| 9 | 3 | 40 | 2.0469243110 | 2.0512820513 | |
| 9 | 3 | 41 | 2.0442185819 | 2.0500000000 | |
| 9 | 3 | 42 | 2.0418779229 | 2.0487804879 | |
| 9 | 3 | 43 | 2.0387148191 | 2.0476190477 | |
| 9 | 3 | 44 | 2.0360672335 | 2.0465116280 | |
| 9 | 3 | 45 | 2.0338627125 | 2.0454545455 | |
| ∗ 9 | 3 | 46 | 1.9999999999 | 2.0000000000 | |
| ∗ 9 | 3 | 47 | 1.9999999999 | 2.0000000000 | |
| ∗ 9 | 3 | 48 | 1.9999999999 | 2.0000000000 | |
| ∗ 9 | 3 | 49 | 1.9999999999 | 2.0000000000 | |
| ∗ 9 | 3 | 50 | 1.9999999999 | 2.0000000000 | |
| ∗ 9 | 3 | 51 | 1.9999999999 | 2.0000000000 | |
| 9 | 3 | 52 | 1.9984293284 | 2.0000000000 | |
| 9 | 3 | 53 | 1.9950018974 | 2.0000000000 | |
| 9 | 3 | 54 | 1.9931008689 | 2.0000000000 | |
| 9 | 3 | 55 | 1.9898017394 | 2.0000000000 | |
| 9 | 3 | 56 | 1.9873031741 | 2.0000000000 | |
| 9 | 3 | 57 | 1.9836029246 | 2.0000000000 | |
| 9 | 3 | 58 | 1.9817423720 | 2.0000000000 | |
| 9 | 3 | 59 | 1.9785568766 | 2.0000000000 | |
| 9 | 3 | 60 | 1.9762907171 | 2.0000000000 | |
| 9 | 3 | 61 | 1.9738963208 | 2.0000000000 | |
| 9 | 3 | 62 | 1.9725766269 | 2.0000000000 | |
| 9 | 3 | 63 | 1.9695351554 | 2.0000000000 | |
| 9 | 3 | 64 | 1.9678642523 | 2.0000000000 | |
| 9 | 3 | 65 | 1.9654932026 | 2.0000000000 | |
| 9 | 3 | 66 | 1.9642618203 | 2.0000000000 | |
| 9 | 3 | 67 | 1.9489822954 | 2.0000000000 | |
| 9 | 3 | 68 | 1.9424076979 | 2.0000000000 | |
| 9 | 3 | 69 | 1.9351112904 | 2.0000000000 | |
| 9 | 3 | 70 | 1.9309759442 | 2.0000000000 | |
| 9 | 3 | 71 | 1.9275473036 | 2.0000000000 | |
| 9 | 3 | 72 | 1.9240710698 | 2.0000000000 | |
| 9 | 3 | 73 | 1.9208990561 | 2.0000000000 | |
| 9 | 3 | 74 | 1.9180931895 | 2.0000000000 | |
| 9 | 3 | 75 | 1.9150736484 | 2.0000000000 | |
| 9 | 3 | 76 | 1.9125739602 | 2.0000000000 | |
| 9 | 3 | 77 | 1.9107035475 | 2.0000000000 | |
| 9 | 3 | 78 | 1.9081499003 | 2.0000000000 | |
| 9 | 3 | 79 | 1.9062226986 | 2.0000000000 | |
| 9 | 3 | 80 | 1.9041204990 | 2.0000000000 | |
| 9 | 3 | 81 | 1.9015683663 | 2.0000000000 | |
| 9 | 3 | 82 | 1.8996278885 | 2.0000000000 | |
| 9 | 3 | 83 | 1.8977358798 | 2.0000000000 | |
| 9 | 3 | 84 | 1.8951541982 | 2.0000000000 | |
| 9 | 3 | 85 | 1.8930631321 | 2.0000000000 | |
| 9 | 3 | 86 | 1.8910014140 | 2.0000000000 | |
| 9 | 3 | 87 | 1.8894551350 | 2.0000000000 | |
| 9 | 3 | 88 | 1.8880586219 | 2.0000000000 | |
| 9 | 3 | 89 | 1.8853134879 | ||
| 9 | 3 | 90 | 1.8835436182 | ||
| 9 | 3 | 91 | 1.8817249589 | ||
| 9 | 3 | 92 | 1.8795075903 | ||
| 9 | 3 | 93 | 1.8776970877 | ||
| 9 | 3 | 94 | 1.8758713477 | ||
| 9 | 3 | 95 | 1.8745919667 | ||
| 9 | 3 | 96 | 1.8726064384 | ||
| 9 | 3 | 97 | 1.8709070056 | ||
| 9 | 3 | 98 | 1.8686909611 | ||
| 9 | 3 | 99 | 1.8667703641 | ||
| 9 | 3 | 100 | 1.8654002384 | ||
| 9 | 4 | 45 | 2.2702890237 | 2.2727272728 | |
| ∗ 9 | 4 | 46 | 2.2222222222 | 2.2222222223 | |
| ∗ 9 | 4 | 49 | 2.2222222222 | 2.2222222223 | |
| 9 | 4 | 50 | 2.2199000776 | 2.2222222223 | |
| 9 | 4 | 51 | 2.2191449223 | 2.2222222223 | |
| 9 | 4 | 52 | 2.2165873022 | 2.2222222223 | |
| 9 | 4 | 53 | 2.2149833364 | 2.2222222223 | |
| 9 | 4 | 54 | 2.2112042717 | 2.2222222223 | |
| 9 | 4 | 55 | 2.2093119084 | 2.2222222223 | |
| 9 | 4 | 56 | 2.2053172071 | 2.2222222223 | |
| 9 | 4 | 57 | 2.2024293207 | 2.2222222223 | |
| 9 | 4 | 58 | 2.1979713031 | 2.2222222223 | |
| 9 | 4 | 59 | 2.1951384177 | 2.2222222223 | |
| 9 | 4 | 60 | 2.1904527705 | 2.2222222223 | |
| 9 | 4 | 61 | 2.1871421708 | 2.2222222223 | |
| 9 | 4 | 62 | 2.1834062961 | 2.2222222223 | |
| 9 | 4 | 63 | 2.1805350811 | 2.2222222223 | |
| 9 | 4 | 64 | 2.1774821057 | 2.2222222223 | |
| 9 | 4 | 65 | 2.1749841002 | 2.2222222223 | |
| 9 | 4 | 66 | 2.1724998803 | 2.2222222223 | |
| 9 | 4 | 67 | 2.1696099947 | 2.2222222223 | |
| 9 | 4 | 68 | 2.1666547763 | 2.2222222223 | |
| 9 | 4 | 69 | 2.1644442256 | 2.2222222223 | |
| 9 | 4 | 70 | 2.1619476026 | 2.2222222223 | |
| 9 | 4 | 71 | 2.1592223048 | 2.2222222223 | |
| 9 | 4 | 72 | 2.1563486436 | 2.2222222223 | |
| 9 | 4 | 73 | 2.1539972410 | 2.2222222223 | |
| 9 | 4 | 74 | 2.1512151042 | 2.2222222223 | |
| 9 | 4 | 75 | 2.1489487984 | 2.2222222223 | |
| 9 | 4 | 76 | 2.1464362472 | 2.2222222223 | |
| 9 | 4 | 77 | 2.1441764769 | 2.2222222223 | |
| 9 | 4 | 78 | 2.1416475895 | 2.2222222223 | |
| 9 | 4 | 79 | 2.1393028788 | 2.2222222223 | |
| 9 | 4 | 80 | 2.1369777169 | 2.2222222223 | |
| 9 | 4 | 81 | 2.1344900175 | 2.2222222223 | |
| 9 | 4 | 82 | 2.1325548006 | 2.2222222223 | |
| 9 | 4 | 83 | 2.1297210469 | 2.2222222223 | |
| 9 | 4 | 84 | 2.1271362623 | 2.2222222223 | |
| 9 | 4 | 85 | 2.1247697592 | 2.2222222223 | |
| 9 | 4 | 86 | 2.1226572034 | 2.2222222223 | |
| 9 | 4 | 87 | 2.1198837716 | 2.2222222223 | |
| 9 | 4 | 88 | 2.1173084588 | 2.2222222223 | |
| 9 | 4 | 89 | 2.1150636700 | ||
| 9 | 4 | 90 | 2.1126150409 | ||
| 9 | 4 | 91 | 2.1104506860 | ||
| 9 | 4 | 92 | 2.1082430404 | ||
| 9 | 4 | 93 | 2.1056386736 | ||
| 9 | 4 | 94 | 2.1032219634 | ||
| 9 | 4 | 95 | 2.1005255671 | ||
| 9 | 4 | 96 | 2.0986926180 | ||
| 9 | 4 | 97 | 2.0966694728 | ||
| 9 | 4 | 98 | 2.0941543367 | ||
| 9 | 4 | 99 | 2.0916262173 | ||
| 9 | 4 | 100 | 2.0900965624 | ||
| ∗ 10 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 10 | 1 | 11 | 0.9899999999 | 0.9900000000 | tight bound |
| 10 | 1 | 12 | 0.9795918367 | 0.9818181819 | |
| 10 | 1 | 13 | 0.9701610293 | 0.9750000000 | |
| 10 | 1 | 14 | 0.9636927022 | 0.9692307693 | Henry Cohn [2] |
| 10 | 1 | 15 | 0.9620836879 | 0.9642857143 | |
| ∗ 10 | 1 | 16 | 0.9599999999 | 0.9600000000 | tight bound |
| 10 | 1 | 17 | 0.9507194976 | 0.9562500000 | |
| 10 | 1 | 18 | 0.9498198614 | 0.9529411765 | |
| 10 | 1 | 19 | 0.9444444444 | 0.9500000000 | |
| 10 | 1 | 20 | 0.9444444444 | 0.9473684211 | |
| 10 | 1 | 21 | 0.9360119154 | 0.9450000000 | Henry Cohn, 2025 |
| 10 | 1 | 22 | 0.9347733958 | 0.9428571429 | Henry Cohn, 2025 |
| 10 | 1 | 23 | 0.9313366956 | 0.9409090910 | Henry Cohn, 2024 |
| 10 | 1 | 24 | 0.9310333458 | 0.9391304348 | Henry Cohn, 2025 |
| 10 | 1 | 25 | 0.9300502194 | 0.9375000000 | |
| 10 | 1 | 26 | 0.9297012650 | 0.9360000000 | Henry Cohn, 2025 |
| 10 | 1 | 27 | 0.9242201266 | 0.9346153847 | Henry Cohn, 2025 |
| 10 | 1 | 28 | 0.9194378816 | 0.9333333334 | Henry Cohn, 2025 |
| 10 | 1 | 29 | 0.9172571846 | 0.9321428572 | |
| 10 | 1 | 30 | 0.9132057633 | 0.9310344828 | Henry Cohn, 2025 |
| 10 | 1 | 31 | 0.9113368360 | 0.9300000000 | |
| 10 | 1 | 32 | 0.9109456444 | 0.9290322581 | |
| 10 | 1 | 33 | 0.9093855333 | 0.9281250000 | Henry Cohn, 2024 |
| 10 | 1 | 34 | 0.9093191976 | 0.9272727273 | |
| 10 | 1 | 35 | 0.9092937388 | 0.9264705883 | |
| 10 | 1 | 36 | 0.9053254437 | 0.9257142858 | |
| 10 | 1 | 37 | 0.9053254437 | 0.9250000000 | |
| 10 | 1 | 38 | 0.9053254437 | 0.9243243244 | |
| 10 | 1 | 39 | 0.9053254437 | 0.9236842106 | |
| 10 | 1 | 40 | 0.9053254437 | 0.9230769231 | |
| 10 | 1 | 41 | 0.8957145195 | 0.9225000000 | Henry Cohn, 2025 |
| 10 | 1 | 42 | 0.8939495669 | 0.9219512196 | Henry Cohn, 2025 |
| 10 | 1 | 43 | 0.8927938263 | 0.9214285715 | Henry Cohn, 2025 |
| 10 | 1 | 44 | 0.8920028799 | 0.9209302326 | Henry Cohn, 2024 |
| 10 | 1 | 45 | 0.8913396196 | 0.9204545455 | Henry Cohn, 2024 |
| 10 | 1 | 46 | 0.8908361510 | 0.9200000000 | Henry Cohn, 2024 |
| 10 | 1 | 47 | 0.8904450865 | 0.9195652174 | |
| 10 | 1 | 48 | 0.8899119241 | 0.9191489362 | Henry Cohn, 2024 |
| 10 | 1 | 49 | 0.8897254046 | 0.9187500000 | |
| 10 | 1 | 50 | 0.8892491841 | 0.9183673470 | |
| 10 | 1 | 51 | 0.8888889116 | 0.9180000000 | |
| 10 | 1 | 52 | 0.8888888891 | 0.9176470589 | |
| 10 | 1 | 53 | 0.8888888888 | 0.9173076924 | |
| 10 | 1 | 54 | 0.8888888888 | 0.9169811321 | |
| 10 | 1 | 55 | 0.8828740780 | 0.9166666667 | |
| 10 | 1 | 56 | 0.8791307488 | 0.9000000000 | |
| 10 | 1 | 57 | 0.8759516737 | 0.9000000000 | |
| 10 | 1 | 58 | 0.8734902536 | 0.9000000000 | |
| 10 | 1 | 59 | 0.8671082052 | 0.9000000000 | |
| 10 | 1 | 60 | 0.8656621045 | 0.9000000000 | |
| 10 | 1 | 61 | 0.8648361193 | 0.9000000000 | Henry Cohn, 2024 |
| 10 | 1 | 62 | 0.8615179785 | 0.9000000000 | |
| 10 | 1 | 63 | 0.8615179785 | 0.9000000000 | |
| 10 | 1 | 64 | 0.8615267654 | 0.9000000000 | Henry Cohn, 2024 |
| 10 | 1 | 65 | 0.8615179785 | 0.9000000000 | |
| 10 | 1 | 66 | 0.8518325826 | 0.9000000000 | |
| 10 | 1 | 67 | 0.8465264471 | 0.9000000000 | |
| 10 | 1 | 68 | 0.8439094495 | 0.9000000000 | |
| 10 | 1 | 69 | 0.8402881286 | 0.9000000000 | |
| 10 | 1 | 70 | 0.8377590617 | 0.9000000000 | |
| 10 | 1 | 71 | 0.8356809302 | 0.9000000000 | |
| 10 | 1 | 72 | 0.8333872517 | 0.9000000000 | |
| 10 | 1 | 73 | 0.8312368159 | 0.9000000000 | |
| 10 | 1 | 74 | 0.8291032400 | 0.9000000000 | |
| 10 | 1 | 75 | 0.8272035407 | 0.9000000000 | |
| 10 | 1 | 76 | 0.8252346390 | 0.9000000000 | |
| 10 | 1 | 77 | 0.8233137114 | 0.9000000000 | |
| 10 | 1 | 78 | 0.8212797061 | 0.9000000000 | |
| 10 | 1 | 79 | 0.8194446490 | 0.9000000000 | |
| 10 | 1 | 80 | 0.8174896636 | 0.9000000000 | |
| 10 | 1 | 81 | 0.8156633388 | 0.9000000000 | |
| 10 | 1 | 82 | 0.8140735185 | 0.9000000000 | |
| 10 | 1 | 83 | 0.8119735528 | 0.9000000000 | |
| 10 | 1 | 84 | 0.8101076725 | 0.9000000000 | |
| 10 | 1 | 85 | 0.8081885001 | 0.9000000000 | |
| 10 | 1 | 86 | 0.8068789347 | 0.9000000000 | |
| 10 | 1 | 87 | 0.8047338178 | 0.9000000000 | |
| 10 | 1 | 88 | 0.8031578077 | 0.9000000000 | |
| 10 | 1 | 89 | 0.8012902268 | 0.9000000000 | |
| 10 | 1 | 90 | 0.7996622387 | 0.9000000000 | |
| 10 | 1 | 91 | 0.7978732500 | 0.9000000000 | |
| 10 | 1 | 92 | 0.7962471644 | 0.9000000000 | |
| 10 | 1 | 93 | 0.7947808729 | 0.9000000000 | |
| 10 | 1 | 94 | 0.7932622387 | 0.9000000000 | |
| 10 | 1 | 95 | 0.7916865927 | 0.9000000000 | |
| 10 | 1 | 96 | 0.7902908007 | 0.9000000000 | |
| 10 | 1 | 97 | 0.7889776287 | 0.9000000000 | |
| 10 | 1 | 98 | 0.7873628662 | 0.9000000000 | |
| 10 | 1 | 99 | 0.7860156893 | 0.9000000000 | |
| 10 | 1 | 100 | 0.7846677264 | 0.9000000000 | |
| ∗ 10 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 10 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 10 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 10 | 2 | 6 | 1.9199999999 | 1.9200000000 | |
| ∗ 10 | 2 | 7 | 1.8666666666 | 1.8666666667 | |
| ∗ 10 | 2 | 8 | 1.8285714285 | 1.8285714286 | |
| ∗ 10 | 2 | 9 | 1.7999999999 | 1.8000000000 | |
| ∗ 10 | 2 | 10 | 1.7777777777 | 1.7777777778 | |
| ∗ 10 | 2 | 11 | 1.7599999999 | 1.7600000000 | |
| ∗ 10 | 2 | 12 | 1.7454545454 | 1.7454545455 | |
| ∗ 10 | 2 | 13 | 1.7333333333 | 1.7333333334 | |
| ∗ 10 | 2 | 14 | 1.7230769230 | 1.7230769231 | |
| ∗ 10 | 2 | 15 | 1.7142857142 | 1.7142857143 | |
| ∗ 10 | 2 | 16 | 1.7066666666 | 1.7066666667 | |
| ∗ 10 | 2 | 17 | 1.6999999999 | 1.7000000000 | |
| ∗ 10 | 2 | 18 | 1.6941176470 | 1.6941176471 | |
| ∗ 10 | 2 | 19 | 1.6888888888 | 1.6888888889 | |
| ∗ 10 | 2 | 20 | 1.6842105263 | 1.6842105264 | |
| ∗ 10 | 2 | 21 | 1.6799999999 | 1.6800000000 | |
| ∗ 10 | 2 | 22 | 1.6761904761 | 1.6761904762 | |
| ∗ 10 | 2 | 23 | 1.6727272727 | 1.6727272728 | |
| ∗ 10 | 2 | 24 | 1.6695652173 | 1.6695652174 | |
| ∗ 10 | 2 | 25 | 1.6666666666 | 1.6666666667 | |
| ∗ 10 | 2 | 26 | 1.6639999999 | 1.6640000000 | |
| ∗ 10 | 2 | 27 | 1.6615384615 | 1.6615384616 | |
| 10 | 2 | 28 | 1.6592592579 | 1.6592592593 | unclear whether bound is tight |
| 10 | 2 | 29 | 1.6571340790 | 1.6571428572 | |
| 10 | 2 | 30 | 1.6551615886 | 1.6551724138 | |
| 10 | 2 | 31 | 1.6526911663 | 1.6533333334 | |
| 10 | 2 | 32 | 1.6501214922 | 1.6516129033 | |
| 10 | 2 | 33 | 1.6476071575 | 1.6500000000 | |
| 10 | 2 | 34 | 1.6448230004 | 1.6484848485 | |
| 10 | 2 | 35 | 1.6431402003 | 1.6470588236 | |
| 10 | 2 | 36 | 1.6414125736 | 1.6457142858 | |
| 10 | 2 | 37 | 1.6363604829 | 1.6444444445 | |
| 10 | 2 | 38 | 1.6333875451 | 1.6432432433 | |
| 10 | 2 | 39 | 1.6305059352 | 1.6421052632 | |
| 10 | 2 | 40 | 1.6289427497 | 1.6410256411 | |
| 10 | 2 | 41 | 1.6241829838 | 1.6400000000 | |
| 10 | 2 | 42 | 1.6213302069 | 1.6390243903 | |
| 10 | 2 | 43 | 1.6191937976 | 1.6380952381 | |
| 10 | 2 | 44 | 1.6174406044 | 1.6372093024 | |
| 10 | 2 | 45 | 1.6159735561 | 1.6363636364 | |
| 10 | 2 | 46 | 1.6102776613 | 1.6355555556 | |
| 10 | 2 | 47 | 1.6071783428 | 1.6347826087 | |
| 10 | 2 | 48 | 1.6047826798 | 1.6340425532 | |
| 10 | 2 | 49 | 1.6018680635 | 1.6333333334 | |
| 10 | 2 | 50 | 1.6003198832 | 1.6326530613 | |
| 10 | 2 | 51 | 1.5959904317 | 1.6320000000 | |
| 10 | 2 | 52 | 1.5928743586 | 1.6313725491 | |
| 10 | 2 | 53 | 1.5903424666 | 1.6307692308 | |
| 10 | 2 | 54 | 1.5878030706 | 1.6301886793 | |
| 10 | 2 | 55 | 1.5856621623 | 1.6296296297 | |
| 10 | 2 | 56 | 1.5808404314 | 1.6000000000 | |
| 10 | 2 | 57 | 1.5764429498 | 1.6000000000 | |
| 10 | 2 | 58 | 1.5729631504 | 1.6000000000 | |
| 10 | 2 | 59 | 1.5699537159 | 1.6000000000 | |
| 10 | 2 | 60 | 1.5663909396 | 1.6000000000 | |
| 10 | 2 | 61 | 1.5633862851 | 1.6000000000 | |
| 10 | 2 | 62 | 1.5600773709 | 1.6000000000 | |
| 10 | 2 | 63 | 1.5580723918 | 1.6000000000 | |
| 10 | 2 | 64 | 1.5548301659 | 1.6000000000 | |
| 10 | 2 | 65 | 1.5519937668 | 1.6000000000 | |
| 10 | 2 | 66 | 1.5491691665 | 1.6000000000 | |
| 10 | 2 | 67 | 1.5469978080 | 1.6000000000 | |
| 10 | 2 | 68 | 1.5438595566 | 1.6000000000 | |
| 10 | 2 | 69 | 1.5414622789 | 1.6000000000 | |
| 10 | 2 | 70 | 1.5396647731 | 1.6000000000 | |
| 10 | 2 | 71 | 1.5373218085 | 1.6000000000 | |
| 10 | 2 | 72 | 1.5346427051 | 1.6000000000 | |
| 10 | 2 | 73 | 1.5325277861 | 1.6000000000 | |
| 10 | 2 | 74 | 1.5301942990 | 1.6000000000 | |
| 10 | 2 | 75 | 1.5276355521 | 1.6000000000 | |
| 10 | 2 | 76 | 1.5256153515 | 1.6000000000 | |
| 10 | 2 | 77 | 1.5237073974 | 1.6000000000 | |
| 10 | 2 | 78 | 1.5220752312 | 1.6000000000 | |
| 10 | 2 | 79 | 1.5196367998 | 1.6000000000 | |
| 10 | 2 | 80 | 1.5174375676 | 1.6000000000 | |
| 10 | 2 | 81 | 1.5167871338 | 1.6000000000 | |
| 10 | 2 | 82 | 1.5133959708 | 1.6000000000 | |
| 10 | 2 | 83 | 1.5117589629 | 1.6000000000 | |
| 10 | 2 | 84 | 1.5098688401 | 1.6000000000 | |
| 10 | 2 | 85 | 1.5081412015 | 1.6000000000 | |
| 10 | 2 | 86 | 1.5062761226 | 1.6000000000 | |
| 10 | 2 | 87 | 1.5046556636 | 1.6000000000 | |
| 10 | 2 | 88 | 1.5027099984 | 1.6000000000 | |
| 10 | 2 | 89 | 1.5006668001 | 1.6000000000 | |
| 10 | 2 | 90 | 1.5001335752 | 1.6000000000 | |
| 10 | 2 | 91 | 1.4973830935 | 1.6000000000 | |
| 10 | 2 | 92 | 1.4958078219 | 1.6000000000 | |
| 10 | 2 | 93 | 1.4940103463 | 1.6000000000 | |
| 10 | 2 | 94 | 1.4929204887 | 1.6000000000 | |
| 10 | 2 | 95 | 1.4907527668 | 1.6000000000 | |
| 10 | 2 | 96 | 1.4894028815 | 1.6000000000 | |
| 10 | 2 | 97 | 1.4877643860 | 1.6000000000 | |
| 10 | 2 | 98 | 1.4865133046 | 1.6000000000 | |
| 10 | 2 | 99 | 1.4847365072 | 1.6000000000 | |
| 10 | 2 | 100 | 1.4829440759 | 1.6000000000 | |
| ∗ 10 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| 10 | 3 | 4 | 2.7777777777 | 2.8000000000 | |
| ∗ 10 | 3 | 5 | 2.6249999999 | 2.6250000000 | |
| ∗ 10 | 3 | 6 | 2.5199999999 | 2.5200000000 | |
| ∗ 10 | 3 | 7 | 2.4499999999 | 2.4500000000 | |
| ∗ 10 | 3 | 8 | 2.3999999999 | 2.4000000000 | |
| ∗ 10 | 3 | 9 | 2.3624999999 | 2.3625000000 | |
| ∗ 10 | 3 | 10 | 2.3333333333 | 2.3333333334 | |
| ∗ 10 | 3 | 11 | 2.3099999999 | 2.3100000000 | |
| ∗ 10 | 3 | 12 | 2.2909090909 | 2.2909090910 | |
| ∗ 10 | 3 | 13 | 2.2749999999 | 2.2750000000 | |
| ∗ 10 | 3 | 14 | 2.2615384615 | 2.2615384616 | |
| ∗ 10 | 3 | 15 | 2.2499999999 | 2.2500000000 | |
| ∗ 10 | 3 | 16 | 2.2399999999 | 2.2400000000 | |
| ∗ 10 | 3 | 17 | 2.2312499999 | 2.2312500000 | |
| ∗ 10 | 3 | 18 | 2.2235294117 | 2.2235294118 | |
| ∗ 10 | 3 | 19 | 2.2166666666 | 2.2166666667 | |
| ∗ 10 | 3 | 20 | 2.2105263157 | 2.2105263158 | |
| ∗ 10 | 3 | 21 | 2.2049999999 | 2.2050000000 | |
| ∗ 10 | 3 | 22 | 2.1999999999 | 2.2000000000 | |
| ∗ 10 | 3 | 23 | 2.1954545454 | 2.1954545455 | |
| ∗ 10 | 3 | 24 | 2.1913043478 | 2.1913043479 | |
| ∗ 10 | 3 | 25 | 2.1874999999 | 2.1875000000 | |
| ∗ 10 | 3 | 26 | 2.1839999999 | 2.1840000000 | |
| ∗ 10 | 3 | 27 | 2.1807692307 | 2.1807692308 | |
| ∗ 10 | 3 | 28 | 2.1777777777 | 2.1777777778 | |
| ∗ 10 | 3 | 29 | 2.1749999999 | 2.1750000000 | |
| ∗ 10 | 3 | 30 | 2.1724137931 | 2.1724137932 | |
| ∗ 10 | 3 | 31 | 2.1699999999 | 2.1700000000 | |
| ∗ 10 | 3 | 32 | 2.1677419354 | 2.1677419355 | |
| ∗ 10 | 3 | 33 | 2.1656249999 | 2.1656250000 | |
| ∗ 10 | 3 | 34 | 2.1636363636 | 2.1636363637 | |
| ∗ 10 | 3 | 35 | 2.1617647058 | 2.1617647059 | |
| ∗ 10 | 3 | 36 | 2.1599999999 | 2.1600000000 | |
| ∗ 10 | 3 | 37 | 2.1583333333 | 2.1583333334 | |
| ∗ 10 | 3 | 38 | 2.1567567567 | 2.1567567568 | |
| 10 | 3 | 39 | 2.1552631573 | 2.1552631579 | unclear whether bound is tight |
| 10 | 3 | 40 | 2.1538461537 | 2.1538461539 | unclear whether bound is tight |
| 10 | 3 | 41 | 2.1524272729 | 2.1525000000 | |
| 10 | 3 | 42 | 2.1507755724 | 2.1512195122 | |
| 10 | 3 | 43 | 2.1489241529 | 2.1500000000 | |
| 10 | 3 | 44 | 2.1470167707 | 2.1488372094 | |
| 10 | 3 | 45 | 2.1460506167 | 2.1477272728 | |
| 10 | 3 | 46 | 2.1428403438 | 2.1466666667 | |
| 10 | 3 | 47 | 2.1408372390 | 2.1456521740 | |
| 10 | 3 | 48 | 2.1386853443 | 2.1446808511 | |
| 10 | 3 | 49 | 2.1363213718 | 2.1437500000 | |
| 10 | 3 | 50 | 2.1348742241 | 2.1428571429 | |
| 10 | 3 | 51 | 2.1317636534 | 2.1420000000 | |
| 10 | 3 | 52 | 2.1291440072 | 2.1411764706 | |
| 10 | 3 | 53 | 2.1270093716 | 2.1403846154 | |
| 10 | 3 | 54 | 2.1242330491 | 2.1396226416 | |
| 10 | 3 | 55 | 2.1225941432 | 2.1388888889 | |
| ∗ 10 | 3 | 56 | 2.0999999999 | 2.1000000000 | |
| ∗ 10 | 3 | 57 | 2.0999999999 | 2.1000000000 | |
| 10 | 3 | 58 | 2.0982220842 | 2.1000000000 | |
| 10 | 3 | 59 | 2.0941097874 | 2.1000000000 | |
| 10 | 3 | 60 | 2.0908591926 | 2.1000000000 | |
| 10 | 3 | 61 | 2.0886972821 | 2.1000000000 | |
| 10 | 3 | 62 | 2.0852593543 | 2.1000000000 | |
| 10 | 3 | 63 | 2.0820779459 | 2.1000000000 | |
| 10 | 3 | 64 | 2.0794150719 | 2.1000000000 | |
| 10 | 3 | 65 | 2.0764956398 | 2.1000000000 | |
| 10 | 3 | 66 | 2.0740027279 | 2.1000000000 | |
| 10 | 3 | 67 | 2.0711376926 | 2.1000000000 | |
| 10 | 3 | 68 | 2.0682239168 | 2.1000000000 | |
| 10 | 3 | 69 | 2.0652575463 | 2.1000000000 | |
| 10 | 3 | 70 | 2.0632777184 | 2.1000000000 | |
| 10 | 3 | 71 | 2.0602115192 | 2.1000000000 | |
| 10 | 3 | 72 | 2.0578406812 | 2.1000000000 | |
| 10 | 3 | 73 | 2.0551236021 | 2.1000000000 | |
| 10 | 3 | 74 | 2.0526479420 | 2.1000000000 | |
| 10 | 3 | 75 | 2.0504215288 | 2.1000000000 | |
| 10 | 3 | 76 | 2.0469296099 | 2.1000000000 | |
| 10 | 3 | 77 | 2.0453815945 | 2.1000000000 | |
| 10 | 3 | 78 | 2.0423625234 | 2.1000000000 | |
| 10 | 3 | 79 | 2.0399402443 | 2.1000000000 | |
| 10 | 3 | 80 | 2.0373373967 | 2.1000000000 | |
| 10 | 3 | 81 | 2.0347083977 | 2.1000000000 | |
| 10 | 3 | 82 | 2.0316126190 | 2.1000000000 | |
| 10 | 3 | 83 | 2.0298409303 | 2.1000000000 | |
| 10 | 3 | 84 | 2.0275202135 | 2.1000000000 | |
| 10 | 3 | 85 | 2.0247305984 | 2.1000000000 | |
| 10 | 3 | 86 | 2.0224463066 | 2.1000000000 | |
| 10 | 3 | 87 | 2.0204046434 | 2.1000000000 | |
| 10 | 3 | 88 | 2.0185419465 | 2.1000000000 | |
| 10 | 3 | 89 | 2.0160407702 | 2.1000000000 | |
| 10 | 3 | 90 | 2.0142004450 | 2.1000000000 | |
| 10 | 3 | 91 | 2.0123777727 | 2.1000000000 | |
| 10 | 3 | 92 | 2.0103730016 | 2.1000000000 | |
| 10 | 3 | 93 | 2.0090991605 | 2.1000000000 | |
| 10 | 3 | 94 | 2.0066559224 | 2.1000000000 | |
| 10 | 3 | 95 | 2.0049473405 | 2.1000000000 | |
| 10 | 3 | 96 | 2.0031172251 | 2.1000000000 | |
| 10 | 3 | 97 | 2.0014736136 | 2.1000000000 | |
| 10 | 3 | 98 | 1.9996120976 | 2.1000000000 | |
| 10 | 3 | 99 | 1.9979765465 | 2.1000000000 | |
| 10 | 3 | 100 | 1.9965698745 | 2.1000000000 | |
| 10 | 4 | 50 | 2.4474833415 | 2.4489795919 | |
| 10 | 4 | 51 | 2.4455409430 | 2.4480000000 | |
| 10 | 4 | 52 | 2.4437200830 | 2.4470588236 | |
| 10 | 4 | 53 | 2.4418267360 | 2.4461538462 | |
| 10 | 4 | 54 | 2.4400548844 | 2.4452830189 | |
| 10 | 4 | 55 | 2.4386745754 | 2.4444444445 | |
| ∗ 10 | 4 | 56 | 2.3999999999 | 2.4000000000 | |
| ∗ 10 | 4 | 57 | 2.3999999999 | 2.4000000000 | |
| ∗ 10 | 4 | 58 | 2.3999999999 | 2.4000000000 | |
| ∗ 10 | 4 | 59 | 2.3999999999 | 2.4000000000 | |
| 10 | 4 | 60 | 2.3999564632 | 2.4000000000 | |
| 10 | 4 | 61 | 2.3983678036 | 2.4000000000 | |
| 10 | 4 | 62 | 2.3955678609 | 2.4000000000 | |
| 10 | 4 | 63 | 2.3940044014 | 2.4000000000 | |
| 10 | 4 | 64 | 2.3921986567 | 2.4000000000 | |
| 10 | 4 | 65 | 2.3894501083 | 2.4000000000 | |
| 10 | 4 | 66 | 2.3882249052 | 2.4000000000 | |
| 10 | 4 | 67 | 2.3847618862 | 2.4000000000 | |
| 10 | 4 | 68 | 2.3827128945 | 2.4000000000 | |
| 10 | 4 | 69 | 2.3800213146 | 2.4000000000 | |
| 10 | 4 | 70 | 2.3778961833 | 2.4000000000 | |
| 10 | 4 | 71 | 2.3749558053 | 2.4000000000 | |
| 10 | 4 | 72 | 2.3714853778 | 2.4000000000 | |
| 10 | 4 | 73 | 2.3679740550 | 2.4000000000 | |
| 10 | 4 | 74 | 2.3655093641 | 2.4000000000 | |
| 10 | 4 | 75 | 2.3625990642 | 2.4000000000 | |
| 10 | 4 | 76 | 2.3593470356 | 2.4000000000 | |
| 10 | 4 | 77 | 2.3567286355 | 2.4000000000 | |
| 10 | 4 | 78 | 2.3544660101 | 2.4000000000 | |
| 10 | 4 | 79 | 2.3515429899 | 2.4000000000 | |
| 10 | 4 | 80 | 2.3486626331 | 2.4000000000 | |
| 10 | 4 | 81 | 2.3456776560 | 2.4000000000 | |
| 10 | 4 | 82 | 2.3433965344 | 2.4000000000 | |
| 10 | 4 | 83 | 2.3414269515 | 2.4000000000 | |
| 10 | 4 | 84 | 2.3394304631 | 2.4000000000 | |
| 10 | 4 | 85 | 2.3366452057 | 2.4000000000 | |
| 10 | 4 | 86 | 2.3344306791 | 2.4000000000 | |
| 10 | 4 | 87 | 2.3328021272 | 2.4000000000 | |
| 10 | 4 | 88 | 2.3301513719 | 2.4000000000 | |
| 10 | 4 | 89 | 2.3281777108 | 2.4000000000 | |
| 10 | 4 | 90 | 2.3265130702 | 2.4000000000 | |
| 10 | 4 | 91 | 2.3246401337 | 2.4000000000 | |
| 10 | 4 | 92 | 2.3224053543 | 2.4000000000 | |
| 10 | 4 | 93 | 2.3201125685 | 2.4000000000 | |
| 10 | 4 | 94 | 2.3180839911 | 2.4000000000 | |
| 10 | 4 | 95 | 2.3161610882 | 2.4000000000 | |
| 10 | 4 | 96 | 2.3141982186 | 2.4000000000 | |
| 10 | 4 | 97 | 2.3122017344 | 2.4000000000 | |
| 10 | 4 | 98 | 2.3106247789 | 2.4000000000 | |
| 10 | 4 | 99 | 2.3086381982 | 2.4000000000 | |
| 10 | 4 | 100 | 2.3063778165 | 2.4000000000 | |
| 10 | 5 | 50 | 2.5499773999 | 2.5510204082 | |
| 10 | 5 | 55 | 2.5433584078 | 2.5462962963 | |
| 10 | 5 | 56 | 2.4999999985 | 2.5000000000 | unclear whether bound is tight |
| 10 | 5 | 88 | 2.4999995807 | 2.5000000000 | |
| ∗ 11 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 11 | 1 | 12 | 0.9917355371 | 0.9917355372 | tight bound |
| 11 | 1 | 13 | 0.9817779155 | 0.9848484849 | |
| 11 | 1 | 14 | 0.9751071940 | 0.9790209791 | |
| 11 | 1 | 15 | 0.9696286013 | 0.9740259741 | Henry Cohn [2] |
| 11 | 1 | 16 | 0.9681753716 | 0.9696969697 | |
| 11 | 1 | 17 | 0.9630502549 | 0.9659090910 | |
| 11 | 1 | 18 | 0.9599999999 | 0.9625668450 | |
| 11 | 1 | 19 | 0.9543790921 | 0.9595959596 | Henry Cohn, 2025 |
| 11 | 1 | 20 | 0.9537099157 | 0.9569377991 | Henry Cohn, 2025 |
| 11 | 1 | 21 | 0.9485857426 | 0.9545454546 | |
| 11 | 1 | 22 | 0.9466719366 | 0.9523809524 | |
| 11 | 1 | 23 | 0.9442751814 | 0.9504132232 | Henry Cohn, 2024 |
| 11 | 1 | 24 | 0.9403934453 | 0.9486166008 | Henry Cohn, 2025 |
| 11 | 1 | 25 | 0.9385278686 | 0.9469696970 | Henry Cohn, 2025 |
| 11 | 1 | 26 | 0.9379801645 | 0.9454545455 | |
| 11 | 1 | 27 | 0.9359029921 | 0.9440559441 | |
| 11 | 1 | 28 | 0.9358677170 | 0.9427609428 | Henry Cohn, 2025 |
| 11 | 1 | 29 | 0.9347117305 | 0.9415584416 | Henry Cohn, 2025 |
| 11 | 1 | 30 | 0.9347102627 | 0.9404388715 | |
| 11 | 1 | 31 | 0.9284382907 | 0.9393939394 | |
| 11 | 1 | 32 | 0.9269380546 | 0.9384164223 | |
| 11 | 1 | 33 | 0.9247085866 | 0.9375000000 | Henry Cohn, 2024 |
| 11 | 1 | 34 | 0.9222978157 | 0.9366391185 | Henry Cohn, 2024 |
| 11 | 1 | 35 | 0.9221771420 | 0.9358288771 | Henry Cohn, 2024 |
| 11 | 1 | 36 | 0.9198022830 | 0.9350649351 | Henry Cohn, 2024 |
| 11 | 1 | 37 | 0.9194104805 | 0.9343434344 | Henry Cohn, 2025 |
| 11 | 1 | 38 | 0.9186539797 | 0.9336609337 | |
| 11 | 1 | 39 | 0.9176886291 | 0.9330143541 | Henry Cohn, 2025 |
| 11 | 1 | 40 | 0.9110519677 | 0.9324009325 | Henry Cohn, 2024 |
| 11 | 1 | 41 | 0.9097856506 | 0.9318181819 | Henry Cohn, 2024 |
| 11 | 1 | 42 | 0.9090966500 | 0.9312638581 | Henry Cohn, 2025 |
| 11 | 1 | 43 | 0.9068865456 | 0.9307359308 | Henry Cohn, 2025 |
| 11 | 1 | 44 | 0.9058997074 | 0.9302325582 | Henry Cohn, 2024 |
| 11 | 1 | 45 | 0.9055665436 | 0.9297520662 | Henry Cohn, 2025 |
| 11 | 1 | 46 | 0.9051987820 | 0.9292929293 | Henry Cohn, 2025 |
| 11 | 1 | 47 | 0.9036398976 | 0.9288537550 | |
| 11 | 1 | 48 | 0.9001480078 | 0.9284332689 | Henry Cohn, 2025 |
| 11 | 1 | 49 | 0.8996637148 | 0.9280303031 | Henry Cohn, 2024 |
| 11 | 1 | 50 | 0.8967271884 | 0.9276437848 | Henry Cohn, 2025 |
| 11 | 1 | 51 | 0.8948849784 | 0.9272727273 | |
| 11 | 1 | 52 | 0.8939471783 | 0.9269162211 | |
| 11 | 1 | 53 | 0.8935096402 | 0.9265734266 | |
| 11 | 1 | 54 | 0.8935096402 | 0.9262435678 | |
| 11 | 1 | 55 | 0.8925573930 | 0.9259259260 | |
| 11 | 1 | 56 | 0.8925573930 | 0.9256198348 | |
| 11 | 1 | 57 | 0.8910705268 | 0.9253246754 | |
| 11 | 1 | 58 | 0.8904693173 | 0.9250398725 | |
| 11 | 1 | 59 | 0.8903312723 | 0.9247648903 | |
| 11 | 1 | 60 | 0.8903312723 | 0.9244992296 | |
| 11 | 1 | 61 | 0.8898548216 | 0.9242424243 | |
| 11 | 1 | 62 | 0.8891150779 | 0.9239940388 | |
| 11 | 1 | 63 | 0.8888901191 | 0.9237536657 | |
| 11 | 1 | 64 | 0.8888901191 | 0.9235209236 | |
| 11 | 1 | 65 | 0.8888888890 | 0.9232954546 | Henry Cohn, 2024 |
| 11 | 1 | 66 | 0.8888888888 | 0.9230769231 | |
| 11 | 1 | 67 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 68 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 69 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 70 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 71 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 72 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 73 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 74 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 75 | 0.8888888888 | 0.9090909091 | |
| 11 | 1 | 76 | 0.8888888888 | 0.9090909091 | Henry Cohn, 2024 |
| 11 | 1 | 77 | 0.8888888888 | 0.9090909091 | Henry Cohn, 2024 |
| 11 | 1 | 78 | 0.8888888888 | 0.9090909091 | Henry Cohn, 2024 |
| 11 | 1 | 79 | 0.8582817754 | 0.9090909091 | |
| 11 | 1 | 80 | 0.8565709088 | 0.9090909091 | |
| 11 | 1 | 81 | 0.8543163662 | 0.9090909091 | |
| 11 | 1 | 82 | 0.8519210475 | 0.9090909091 | |
| 11 | 1 | 83 | 0.8498322773 | 0.9090909091 | |
| ∗ 11 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 11 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 11 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| 11 | 2 | 6 | 1.9599999999 | 1.9636363637 | |
| 11 | 2 | 7 | 1.9088129953 | 1.9090909091 | |
| ∗ 11 | 2 | 8 | 1.8701298701 | 1.8701298702 | |
| ∗ 11 | 2 | 9 | 1.8409090909 | 1.8409090910 | |
| ∗ 11 | 2 | 10 | 1.8181818181 | 1.8181818182 | |
| ∗ 11 | 2 | 11 | 1.7999999999 | 1.8000000000 | |
| ∗ 11 | 2 | 12 | 1.7851239669 | 1.7851239670 | |
| ∗ 11 | 2 | 13 | 1.7727272727 | 1.7727272728 | |
| ∗ 11 | 2 | 14 | 1.7622377622 | 1.7622377623 | |
| ∗ 11 | 2 | 15 | 1.7532467532 | 1.7532467533 | |
| ∗ 11 | 2 | 16 | 1.7454545454 | 1.7454545455 | |
| ∗ 11 | 2 | 17 | 1.7386363636 | 1.7386363637 | |
| ∗ 11 | 2 | 18 | 1.7326203208 | 1.7326203209 | |
| ∗ 11 | 2 | 19 | 1.7272727272 | 1.7272727273 | |
| ∗ 11 | 2 | 20 | 1.7224880382 | 1.7224880383 | |
| ∗ 11 | 2 | 21 | 1.7181818181 | 1.7181818182 | |
| ∗ 11 | 2 | 22 | 1.7142857142 | 1.7142857143 | |
| ∗ 11 | 2 | 23 | 1.7107438016 | 1.7107438017 | |
| ∗ 11 | 2 | 24 | 1.7075098814 | 1.7075098815 | |
| ∗ 11 | 2 | 25 | 1.7045454545 | 1.7045454546 | |
| ∗ 11 | 2 | 26 | 1.7018181818 | 1.7018181819 | |
| ∗ 11 | 2 | 27 | 1.6993006993 | 1.6993006994 | |
| ∗ 11 | 2 | 28 | 1.6969696969 | 1.6969696970 | |
| 11 | 2 | 29 | 1.6948051947 | 1.6948051949 | unclear whether bound is tight |
| ∗ 11 | 2 | 30 | 1.6927899686 | 1.6927899687 | |
| ∗ 11 | 2 | 31 | 1.6909090909 | 1.6909090910 | |
| 11 | 2 | 32 | 1.6891487650 | 1.6891495602 | |
| ∗ 11 | 2 | 33 | 1.6874999999 | 1.6875000000 | |
| 11 | 2 | 34 | 1.6858325432 | 1.6859504133 | |
| 11 | 2 | 35 | 1.6838057950 | 1.6844919787 | |
| 11 | 2 | 36 | 1.6817829421 | 1.6831168832 | |
| 11 | 2 | 37 | 1.6797569476 | 1.6818181819 | |
| 11 | 2 | 38 | 1.6775148672 | 1.6805896806 | |
| 11 | 2 | 39 | 1.6754291358 | 1.6794258374 | |
| 11 | 2 | 40 | 1.6732055209 | 1.6783216784 | |
| 11 | 2 | 41 | 1.6712335869 | 1.6772727273 | |
| 11 | 2 | 42 | 1.6697789330 | 1.6762749446 | |
| 11 | 2 | 43 | 1.6690854752 | 1.6753246754 | |
| 11 | 2 | 44 | 1.6687460213 | 1.6744186047 | |
| 11 | 2 | 45 | 1.6633045534 | 1.6735537191 | |
| 11 | 2 | 46 | 1.6597144818 | 1.6727272728 | |
| 11 | 2 | 47 | 1.6573638011 | 1.6719367589 | |
| 11 | 2 | 48 | 1.6547965201 | 1.6711798840 | |
| 11 | 2 | 49 | 1.6522381105 | 1.6704545455 | |
| 11 | 2 | 50 | 1.6497973528 | 1.6697588127 | |
| 11 | 2 | 51 | 1.6464106598 | 1.6690909091 | |
| 11 | 2 | 52 | 1.6440496081 | 1.6684491979 | |
| 11 | 2 | 53 | 1.6415284519 | 1.6678321679 | |
| 11 | 2 | 54 | 1.6399349232 | 1.6672384220 | |
| 11 | 2 | 55 | 1.6372372612 | 1.6666666667 | |
| 11 | 2 | 56 | 1.6351917426 | 1.6661157025 | |
| 11 | 2 | 57 | 1.6328214294 | 1.6655844156 | |
| 11 | 2 | 58 | 1.6303434705 | 1.6650717704 | |
| 11 | 2 | 59 | 1.6287342109 | 1.6645768026 | |
| 11 | 2 | 60 | 1.6268909063 | 1.6640986133 | |
| 11 | 2 | 61 | 1.6241506658 | 1.6636363637 | |
| 11 | 2 | 62 | 1.6221132930 | 1.6631892698 | |
| 11 | 2 | 63 | 1.6201042562 | 1.6627565983 | |
| 11 | 2 | 64 | 1.6180708728 | 1.6623376624 | |
| 11 | 2 | 65 | 1.6159959440 | 1.6619318182 | |
| 11 | 2 | 66 | 1.6147708645 | 1.6615384616 | |
| 11 | 2 | 67 | 1.6107995975 | 1.6363636364 | |
| 11 | 2 | 68 | 1.6080670059 | 1.6363636364 | |
| 11 | 2 | 69 | 1.6051351419 | 1.6363636364 | |
| 11 | 2 | 70 | 1.6028460665 | 1.6363636364 | |
| 11 | 2 | 71 | 1.5999397533 | 1.6363636364 | |
| 11 | 2 | 72 | 1.5977487210 | 1.6363636364 | |
| 11 | 2 | 73 | 1.5952224550 | 1.6363636364 | |
| 11 | 2 | 74 | 1.5930938107 | 1.6363636364 | |
| 11 | 2 | 75 | 1.5910000857 | 1.6363636364 | |
| 11 | 2 | 76 | 1.5885712523 | 1.6363636364 | |
| 11 | 2 | 77 | 1.5863668230 | 1.6363636364 | |
| 11 | 2 | 78 | 1.5844586223 | 1.6363636364 | |
| 11 | 2 | 79 | 1.5822642094 | 1.6363636364 | |
| 11 | 2 | 80 | 1.5800154935 | 1.6363636364 | |
| 11 | 2 | 81 | 1.5786058528 | 1.6363636364 | |
| 11 | 2 | 82 | 1.5764838293 | 1.6363636364 | |
| 11 | 2 | 83 | 1.5744559193 | 1.6363636364 | |
| ∗ 11 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| 11 | 3 | 4 | 2.8888888888 | 2.9090909091 | |
| ∗ 11 | 3 | 5 | 2.7272727272 | 2.7272727273 | |
| ∗ 11 | 3 | 6 | 2.6181818181 | 2.6181818182 | |
| ∗ 11 | 3 | 7 | 2.5454545454 | 2.5454545455 | |
| ∗ 11 | 3 | 8 | 2.4935064935 | 2.4935064936 | |
| ∗ 11 | 3 | 9 | 2.4545454545 | 2.4545454546 | |
| ∗ 11 | 3 | 10 | 2.4242424242 | 2.4242424243 | |
| ∗ 11 | 3 | 11 | 2.3999999999 | 2.4000000000 | |
| ∗ 11 | 3 | 12 | 2.3801652892 | 2.3801652893 | |
| ∗ 11 | 3 | 13 | 2.3636363636 | 2.3636363637 | |
| ∗ 11 | 3 | 14 | 2.3496503496 | 2.3496503497 | |
| ∗ 11 | 3 | 15 | 2.3376623376 | 2.3376623377 | |
| ∗ 11 | 3 | 16 | 2.3272727272 | 2.3272727273 | |
| ∗ 11 | 3 | 17 | 2.3181818181 | 2.3181818182 | |
| ∗ 11 | 3 | 18 | 2.3101604278 | 2.3101604279 | |
| ∗ 11 | 3 | 19 | 2.3030303030 | 2.3030303031 | |
| ∗ 11 | 3 | 20 | 2.2966507177 | 2.2966507178 | |
| ∗ 11 | 3 | 21 | 2.2909090909 | 2.2909090910 | |
| ∗ 11 | 3 | 22 | 2.2857142857 | 2.2857142858 | |
| ∗ 11 | 3 | 23 | 2.2809917355 | 2.2809917356 | |
| ∗ 11 | 3 | 24 | 2.2766798418 | 2.2766798419 | |
| ∗ 11 | 3 | 25 | 2.2727272727 | 2.2727272728 | |
| ∗ 11 | 3 | 26 | 2.2690909090 | 2.2690909091 | |
| ∗ 11 | 3 | 27 | 2.2657342657 | 2.2657342658 | |
| ∗ 11 | 3 | 28 | 2.2626262626 | 2.2626262627 | |
| ∗ 11 | 3 | 29 | 2.2597402597 | 2.2597402598 | |
| ∗ 11 | 3 | 30 | 2.2570532915 | 2.2570532916 | |
| ∗ 11 | 3 | 31 | 2.2545454545 | 2.2545454546 | |
| ∗ 11 | 3 | 32 | 2.2521994134 | 2.2521994135 | |
| ∗ 11 | 3 | 33 | 2.2499999999 | 2.2500000000 | |
| ∗ 11 | 3 | 34 | 2.2479338842 | 2.2479338843 | |
| ∗ 11 | 3 | 35 | 2.2459893048 | 2.2459893049 | |
| ∗ 11 | 3 | 36 | 2.2441558441 | 2.2441558442 | |
| ∗ 11 | 3 | 37 | 2.2424242424 | 2.2424242425 | |
| ∗ 11 | 3 | 38 | 2.2407862407 | 2.2407862408 | |
| ∗ 11 | 3 | 39 | 2.2392344497 | 2.2392344498 | |
| ∗ 11 | 3 | 40 | 2.2377622377 | 2.2377622378 | |
| ∗ 11 | 3 | 41 | 2.2363636363 | 2.2363636364 | |
| ∗ 11 | 3 | 42 | 2.2350332594 | 2.2350332595 | |
| ∗ 11 | 3 | 43 | 2.2337662337 | 2.2337662338 | |
| ∗ 11 | 3 | 44 | 2.2325581395 | 2.2325581396 | |
| ∗ 11 | 3 | 45 | 2.2314049586 | 2.2314049587 | |
| 11 | 3 | 46 | 2.2302986855 | 2.2303030304 | |
| 11 | 3 | 47 | 2.2291085048 | 2.2292490119 | |
| 11 | 3 | 48 | 2.2277692261 | 2.2282398453 | |
| 11 | 3 | 49 | 2.2262599170 | 2.2272727273 | |
| 11 | 3 | 50 | 2.2247217500 | 2.2263450835 | |
| 11 | 3 | 51 | 2.2230842660 | 2.2254545455 | |
| 11 | 3 | 52 | 2.2212218601 | 2.2245989305 | |
| 11 | 3 | 53 | 2.2196062874 | 2.2237762238 | |
| 11 | 3 | 54 | 2.2177727866 | 2.2229845627 | |
| 11 | 3 | 55 | 2.2160562344 | 2.2222222223 | |
| 11 | 3 | 56 | 2.2141803011 | 2.2214876034 | |
| 11 | 3 | 57 | 2.2120800004 | 2.2207792208 | |
| 11 | 3 | 58 | 2.2104652437 | 2.2200956938 | |
| 11 | 3 | 59 | 2.2081263751 | 2.2194357367 | |
| 11 | 3 | 60 | 2.2064567205 | 2.2187981511 | |
| 11 | 3 | 61 | 2.2047061696 | 2.2181818182 | |
| 11 | 3 | 62 | 2.2026570612 | 2.2175856930 | |
| 11 | 3 | 63 | 2.2010545822 | 2.2170087977 | |
| 11 | 3 | 64 | 2.1987523504 | 2.2164502165 | |
| 11 | 3 | 65 | 2.1964480234 | 2.2159090910 | |
| 11 | 3 | 66 | 2.1949295362 | 2.2153846154 | |
| ∗ 11 | 3 | 67 | 2.1818181818 | 2.1818181819 | |
| 11 | 3 | 68 | 2.1796666088 | 2.1818181819 | |
| 11 | 3 | 69 | 2.1760674306 | 2.1818181819 | |
| 11 | 3 | 70 | 2.1724607962 | 2.1818181819 | |
| 11 | 3 | 71 | 2.1696446288 | 2.1818181819 | |
| 11 | 3 | 72 | 2.1670581856 | 2.1818181819 | |
| 11 | 3 | 73 | 2.1648495967 | 2.1818181819 | |
| 11 | 3 | 74 | 2.1621319488 | 2.1818181819 | |
| 11 | 3 | 75 | 2.1596882951 | 2.1818181819 | |
| 11 | 3 | 76 | 2.1573945567 | 2.1818181819 | |
| 11 | 3 | 77 | 2.1549042856 | 2.1818181819 | |
| 11 | 3 | 78 | 2.1526472816 | 2.1818181819 | |
| 11 | 3 | 79 | 2.1504620672 | 2.1818181819 | |
| 11 | 3 | 80 | 2.1482500235 | 2.1818181819 | |
| 11 | 3 | 81 | 2.1463056966 | 2.1818181819 | |
| 11 | 3 | 82 | 2.1437971644 | 2.1818181819 | |
| 11 | 3 | 83 | 2.1399504595 | 2.1818181819 | |
| ∗ 11 | 4 | 51 | 2.5963636363 | 2.5963636364 | |
| ∗ 11 | 4 | 52 | 2.5953654188 | 2.5953654189 | |
| ∗ 11 | 4 | 53 | 2.5944055944 | 2.5944055945 | |
| 11 | 4 | 54 | 2.5934819008 | 2.5934819898 | unclear whether bound is tight |
| 11 | 4 | 55 | 2.5925311289 | 2.5925925926 | |
| 11 | 4 | 56 | 2.5914017299 | 2.5917355372 | |
| 11 | 4 | 57 | 2.5901288704 | 2.5909090910 | |
| 11 | 4 | 58 | 2.5887385732 | 2.5901116428 | |
| 11 | 4 | 59 | 2.5873967458 | 2.5893416928 | |
| 11 | 4 | 60 | 2.5856899129 | 2.5885978429 | |
| 11 | 4 | 61 | 2.5843916118 | 2.5878787879 | |
| 11 | 4 | 62 | 2.5826971612 | 2.5871833085 | |
| 11 | 4 | 63 | 2.5810854763 | 2.5865102640 | |
| 11 | 4 | 64 | 2.5794344419 | 2.5858585859 | |
| 11 | 4 | 65 | 2.5779064189 | 2.5852272728 | |
| 11 | 4 | 66 | 2.5777278197 | 2.5846153847 | |
| ∗ 11 | 4 | 67 | 2.5454545454 | 2.5454545455 | |
| ∗ 11 | 4 | 68 | 2.5454545454 | 2.5454545455 | |
| 11 | 4 | 69 | 2.5454545210 | 2.5454545455 | unclear whether bound is tight |
| 11 | 4 | 70 | 2.5449868775 | 2.5454545455 | |
| 11 | 4 | 71 | 2.5431609725 | 2.5454545455 | |
| 11 | 4 | 72 | 2.5409135202 | 2.5454545455 | |
| 11 | 4 | 73 | 2.5396456987 | 2.5454545455 | |
| 11 | 4 | 74 | 2.5380739779 | 2.5454545455 | |
| 11 | 4 | 75 | 2.5361576030 | 2.5454545455 | |
| 11 | 4 | 76 | 2.5342233677 | 2.5454545455 | |
| 11 | 4 | 77 | 2.5319750609 | 2.5454545455 | |
| 11 | 4 | 78 | 2.5305438055 | 2.5454545455 | |
| 11 | 4 | 79 | 2.5279959454 | 2.5454545455 | |
| 11 | 4 | 80 | 2.5261479193 | 2.5454545455 | |
| 11 | 4 | 81 | 2.5241759911 | 2.5454545455 | |
| 11 | 4 | 82 | 2.5221360342 | 2.5454545455 | |
| 11 | 5 | 66 | 2.7673627240 | 2.7692307693 | |
| ∗ 12 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 12 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 12 | 1 | 13 | 0.9930555555 | 0.9930555556 | tight bound |
| 12 | 1 | 14 | 0.9848824667 | 0.9871794872 | Henry Cohn [2] |
| 12 | 1 | 15 | 0.9786237766 | 0.9821428572 | Henry Cohn [2] |
| 12 | 1 | 16 | 0.9739713440 | 0.9777777778 | |
| 12 | 1 | 17 | 0.9707065575 | 0.9739583334 | |
| 12 | 1 | 18 | 0.9668782708 | 0.9705882353 | Henry Cohn, 2024 |
| 12 | 1 | 19 | 0.9643604126 | 0.9675925926 | Henry Cohn, 2025 |
| 12 | 1 | 20 | 0.9615657985 | 0.9649122808 | Henry Cohn, 2025 |
| 12 | 1 | 21 | 0.9600113891 | 0.9625000000 | Henry Cohn, 2025 |
| 12 | 1 | 22 | 0.9559245905 | 0.9603174604 | |
| 12 | 1 | 23 | 0.9544511501 | 0.9583333334 | |
| 12 | 1 | 24 | 0.9544511501 | 0.9565217392 | |
| 12 | 1 | 25 | 0.9499464805 | 0.9548611112 | Henry Cohn, 2025 |
| 12 | 1 | 26 | 0.9494803514 | 0.9533333334 | Henry Cohn, 2025 |
| 12 | 1 | 27 | 0.9442926249 | 0.9519230770 | Henry Cohn, 2025 |
| 12 | 1 | 28 | 0.9423089463 | 0.9506172840 | Henry Cohn, 2024 |
| 12 | 1 | 29 | 0.9397414052 | 0.9494047620 | Henry Cohn, 2024 |
| 12 | 1 | 30 | 0.9383679899 | 0.9482758621 | Henry Cohn, 2024 |
| 12 | 1 | 31 | 0.9375329142 | 0.9472222223 | Henry Cohn, 2025 |
| 12 | 1 | 32 | 0.9375000444 | 0.9462365592 | |
| 12 | 1 | 33 | 0.9374999999 | 0.9453125000 | |
| 12 | 1 | 34 | 0.9374999999 | 0.9444444445 | |
| 12 | 1 | 35 | 0.9374999999 | 0.9436274510 | |
| 12 | 1 | 36 | 0.9374999999 | 0.9428571429 | |
| 12 | 1 | 37 | 0.9374999999 | 0.9421296297 | |
| 12 | 1 | 38 | 0.9374999999 | 0.9414414415 | |
| 12 | 1 | 39 | 0.9374999999 | 0.9407894737 | |
| 12 | 1 | 40 | 0.9354081173 | 0.9401709402 | |
| 12 | 1 | 41 | 0.9285211720 | 0.9395833334 | |
| 12 | 1 | 42 | 0.9269265447 | 0.9390243903 | |
| 12 | 1 | 43 | 0.9246444992 | 0.9384920635 | Henry Cohn, 2024 |
| 12 | 1 | 44 | 0.9237067193 | 0.9379844962 | Henry Cohn, 2024 |
| 12 | 1 | 45 | 0.9236071603 | 0.9375000000 | Henry Cohn, 2025 |
| 12 | 1 | 46 | 0.9236067977 | 0.9370370371 | |
| 12 | 1 | 47 | 0.9236067977 | 0.9365942029 | |
| 12 | 1 | 48 | 0.9236067977 | 0.9361702128 | |
| 12 | 1 | 49 | 0.9177768416 | 0.9357638889 | |
| 12 | 1 | 50 | 0.9163211204 | 0.9353741497 | Henry Cohn, 2025 |
| 12 | 1 | 51 | 0.9059711300 | 0.9350000000 | |
| 12 | 1 | 52 | 0.9053953200 | 0.9346405229 | |
| 12 | 1 | 53 | 0.9045363823 | 0.9342948718 | |
| 12 | 1 | 54 | 0.9035623652 | 0.9339622642 | |
| 12 | 1 | 55 | 0.9026610548 | 0.9336419754 | |
| 12 | 1 | 56 | 0.9021025138 | 0.9333333334 | |
| 12 | 1 | 57 | 0.9010704788 | 0.9330357143 | |
| 12 | 1 | 58 | 0.9001388249 | 0.9327485381 | |
| 12 | 1 | 59 | 0.8994919322 | 0.9324712644 | |
| 12 | 1 | 60 | 0.8988369188 | 0.9322033899 | |
| 12 | 1 | 61 | 0.8982171518 | 0.9319444445 | |
| 12 | 1 | 62 | 0.8973238261 | 0.9316939891 | |
| 12 | 1 | 63 | 0.8967360791 | 0.9314516130 | |
| 12 | 1 | 64 | 0.8960446076 | 0.9312169313 | |
| 12 | 1 | 65 | 0.8955490203 | 0.9309895834 | |
| 12 | 1 | 66 | 0.8949176305 | 0.9307692308 | |
| 12 | 1 | 67 | 0.8940777222 | 0.9305555556 | |
| 12 | 1 | 68 | 0.8935613463 | 0.9303482588 | |
| 12 | 1 | 69 | 0.8931981598 | 0.9301470589 | |
| 12 | 1 | 70 | 0.8921872714 | 0.9299516909 | |
| 12 | 1 | 71 | 0.8921203940 | 0.9297619048 | |
| 12 | 1 | 72 | 0.8908989892 | 0.9295774648 | |
| 12 | 1 | 73 | 0.8904487563 | 0.9293981482 | |
| 12 | 1 | 74 | 0.8899354943 | 0.9292237443 | |
| 12 | 1 | 75 | 0.8889792736 | 0.9290540541 | |
| 12 | 1 | 76 | 0.8888888888 | 0.9288888889 | |
| 12 | 1 | 77 | 0.8888888888 | 0.9287280702 | |
| 12 | 1 | 78 | 0.8888888888 | 0.9285714286 | |
| 12 | 1 | 79 | 0.8856358863 | 0.9166666667 | |
| 12 | 1 | 80 | 0.8835601501 | 0.9166666667 | |
| 12 | 1 | 81 | 0.8829017669 | 0.9166666667 | |
| 12 | 1 | 82 | 0.8808871355 | 0.9166666667 | |
| 12 | 1 | 83 | 0.8793120150 | 0.9166666667 | |
| 12 | 1 | 84 | 0.8783024099 | 0.9166666667 | |
| 12 | 1 | 85 | 0.8770020029 | 0.9166666667 | |
| 12 | 1 | 86 | 0.8760424784 | 0.9166666667 | |
| 12 | 1 | 87 | 0.8745895765 | 0.9166666667 | |
| 12 | 1 | 88 | 0.8737428740 | 0.9166666667 | |
| 12 | 1 | 89 | 0.8721612459 | 0.9166666667 | |
| 12 | 1 | 90 | 0.8706332749 | 0.9166666667 | |
| 12 | 1 | 91 | 0.8698186584 | 0.9166666667 | |
| 12 | 1 | 92 | 0.8679406193 | 0.9166666667 | |
| 12 | 1 | 93 | 0.8665782618 | 0.9166666667 | |
| 12 | 1 | 94 | 0.8645273436 | 0.9166666667 | |
| ∗ 12 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 12 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 12 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 12 | 2 | 6 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 12 | 2 | 7 | 1.9444444444 | 1.9444444445 | |
| ∗ 12 | 2 | 8 | 1.9047619047 | 1.9047619048 | |
| ∗ 12 | 2 | 9 | 1.8749999999 | 1.8750000000 | |
| ∗ 12 | 2 | 10 | 1.8518518518 | 1.8518518519 | |
| ∗ 12 | 2 | 11 | 1.8333333333 | 1.8333333334 | |
| ∗ 12 | 2 | 12 | 1.8181818181 | 1.8181818182 | |
| ∗ 12 | 2 | 13 | 1.8055555555 | 1.8055555556 | |
| ∗ 12 | 2 | 14 | 1.7948717948 | 1.7948717949 | |
| ∗ 12 | 2 | 15 | 1.7857142857 | 1.7857142858 | |
| ∗ 12 | 2 | 16 | 1.7777777777 | 1.7777777778 | |
| ∗ 12 | 2 | 17 | 1.7708333333 | 1.7708333334 | |
| ∗ 12 | 2 | 18 | 1.7647058823 | 1.7647058824 | |
| ∗ 12 | 2 | 19 | 1.7592592592 | 1.7592592593 | |
| ∗ 12 | 2 | 20 | 1.7543859649 | 1.7543859650 | |
| ∗ 12 | 2 | 21 | 1.7499999999 | 1.7500000000 | |
| ∗ 12 | 2 | 22 | 1.7460317460 | 1.7460317461 | |
| ∗ 12 | 2 | 23 | 1.7424242424 | 1.7424242425 | |
| ∗ 12 | 2 | 24 | 1.7391304347 | 1.7391304348 | |
| ∗ 12 | 2 | 25 | 1.7361111111 | 1.7361111112 | |
| ∗ 12 | 2 | 26 | 1.7333333333 | 1.7333333334 | |
| ∗ 12 | 2 | 27 | 1.7307692307 | 1.7307692308 | |
| ∗ 12 | 2 | 28 | 1.7283950617 | 1.7283950618 | |
| ∗ 12 | 2 | 29 | 1.7261904761 | 1.7261904762 | |
| ∗ 12 | 2 | 30 | 1.7241379310 | 1.7241379311 | |
| ∗ 12 | 2 | 31 | 1.7222222222 | 1.7222222223 | |
| ∗ 12 | 2 | 32 | 1.7204301075 | 1.7204301076 | |
| ∗ 12 | 2 | 33 | 1.7187499999 | 1.7187500000 | |
| ∗ 12 | 2 | 34 | 1.7171717171 | 1.7171717172 | |
| 12 | 2 | 35 | 1.7156862561 | 1.7156862746 | unclear whether bound is tight |
| 12 | 2 | 36 | 1.7142849402 | 1.7142857143 | |
| 12 | 2 | 37 | 1.7128951027 | 1.7129629630 | |
| 12 | 2 | 38 | 1.7114069196 | 1.7117117118 | |
| 12 | 2 | 39 | 1.7097313772 | 1.7105263158 | |
| 12 | 2 | 40 | 1.7082076422 | 1.7094017095 | |
| 12 | 2 | 41 | 1.7063613416 | 1.7083333334 | |
| 12 | 2 | 42 | 1.7047172384 | 1.7073170732 | |
| 12 | 2 | 43 | 1.7028054036 | 1.7063492064 | |
| 12 | 2 | 44 | 1.7021113805 | 1.7054263566 | |
| 12 | 2 | 45 | 1.6991966011 | 1.7045454546 | |
| 12 | 2 | 46 | 1.6973569022 | 1.7037037038 | |
| 12 | 2 | 47 | 1.6959846782 | 1.7028985508 | |
| 12 | 2 | 48 | 1.6947391528 | 1.7021276596 | |
| 12 | 2 | 49 | 1.6917124881 | 1.7013888889 | |
| 12 | 2 | 50 | 1.6897650411 | 1.7006802722 | |
| 12 | 2 | 51 | 1.6869535406 | 1.7000000000 | |
| 12 | 2 | 52 | 1.6851645010 | 1.6993464053 | |
| 12 | 2 | 53 | 1.6834044889 | 1.6987179488 | |
| 12 | 2 | 54 | 1.6817342996 | 1.6981132076 | |
| 12 | 2 | 55 | 1.6795836466 | 1.6975308642 | |
| 12 | 2 | 56 | 1.6774158104 | 1.6969696970 | |
| 12 | 2 | 57 | 1.6755091521 | 1.6964285715 | |
| 12 | 2 | 58 | 1.6736951044 | 1.6959064328 | |
| 12 | 2 | 59 | 1.6718032518 | 1.6954022989 | |
| 12 | 2 | 60 | 1.6699434460 | 1.6949152543 | |
| 12 | 2 | 61 | 1.6680452399 | 1.6944444445 | |
| 12 | 2 | 62 | 1.6661656352 | 1.6939890711 | |
| 12 | 2 | 63 | 1.6643218767 | 1.6935483871 | |
| 12 | 2 | 64 | 1.6624683476 | 1.6931216932 | |
| 12 | 2 | 65 | 1.6605586720 | 1.6927083334 | |
| 12 | 2 | 66 | 1.6588301480 | 1.6923076924 | |
| 12 | 2 | 67 | 1.6572946971 | 1.6919191920 | |
| 12 | 2 | 68 | 1.6557462987 | 1.6915422886 | |
| 12 | 2 | 69 | 1.6535891863 | 1.6911764706 | |
| 12 | 2 | 70 | 1.6518437858 | 1.6908212561 | |
| 12 | 2 | 71 | 1.6500539606 | 1.6904761905 | |
| 12 | 2 | 72 | 1.6484294020 | 1.6901408451 | |
| 12 | 2 | 73 | 1.6469918405 | 1.6898148149 | |
| 12 | 2 | 74 | 1.6453091758 | 1.6894977169 | |
| 12 | 2 | 75 | 1.6433168718 | 1.6891891892 | |
| 12 | 2 | 76 | 1.6419559480 | 1.6888888889 | |
| 12 | 2 | 77 | 1.6399310857 | 1.6885964913 | |
| 12 | 2 | 78 | 1.6391193258 | 1.6883116884 | |
| 12 | 2 | 79 | 1.6366666436 | 1.6666666667 | |
| 12 | 2 | 80 | 1.6341673183 | 1.6666666667 | |
| 12 | 2 | 81 | 1.6320687903 | 1.6666666667 | |
| 12 | 2 | 82 | 1.6302840350 | 1.6666666667 | |
| 12 | 2 | 83 | 1.6281291984 | 1.6666666667 | |
| 12 | 2 | 84 | 1.6263703629 | 1.6666666667 | |
| 12 | 2 | 85 | 1.6242962710 | 1.6666666667 | |
| 12 | 2 | 86 | 1.6228039950 | 1.6666666667 | |
| 12 | 2 | 87 | 1.6208163027 | 1.6666666667 | |
| 12 | 2 | 88 | 1.6187735210 | 1.6666666667 | |
| 12 | 2 | 89 | 1.6171912596 | 1.6666666667 | |
| 12 | 2 | 90 | 1.6156475921 | 1.6666666667 | |
| 12 | 2 | 91 | 1.6138099617 | 1.6666666667 | |
| 12 | 2 | 92 | 1.6122743946 | 1.6666666667 | |
| 12 | 2 | 93 | 1.6104879900 | 1.6666666667 | |
| 12 | 2 | 94 | 1.6091370814 | 1.6666666667 | |
| ∗ 12 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 12 | 3 | 4 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 12 | 3 | 5 | 2.8124999999 | 2.8125000000 | |
| ∗ 12 | 3 | 6 | 2.6999999999 | 2.7000000000 | |
| ∗ 12 | 3 | 7 | 2.6249999999 | 2.6250000000 | |
| ∗ 12 | 3 | 8 | 2.5714285714 | 2.5714285715 | |
| ∗ 12 | 3 | 9 | 2.5312499999 | 2.5312500000 | |
| ∗ 12 | 3 | 10 | 2.4999999999 | 2.5000000000 | |
| ∗ 12 | 3 | 11 | 2.4749999999 | 2.4750000000 | |
| ∗ 12 | 3 | 12 | 2.4545454545 | 2.4545454546 | |
| ∗ 12 | 3 | 13 | 2.4374999999 | 2.4375000000 | |
| ∗ 12 | 3 | 14 | 2.4230769230 | 2.4230769231 | |
| ∗ 12 | 3 | 15 | 2.4107142857 | 2.4107142858 | |
| ∗ 12 | 3 | 16 | 2.3999999999 | 2.4000000000 | |
| ∗ 12 | 3 | 17 | 2.3906249999 | 2.3906250000 | |
| ∗ 12 | 3 | 18 | 2.3823529411 | 2.3823529412 | |
| ∗ 12 | 3 | 19 | 2.3749999999 | 2.3750000000 | |
| ∗ 12 | 3 | 20 | 2.3684210526 | 2.3684210527 | |
| ∗ 12 | 3 | 21 | 2.3624999999 | 2.3625000000 | |
| ∗ 12 | 3 | 22 | 2.3571428571 | 2.3571428572 | |
| ∗ 12 | 3 | 23 | 2.3522727272 | 2.3522727273 | |
| ∗ 12 | 3 | 24 | 2.3478260869 | 2.3478260870 | |
| ∗ 12 | 3 | 25 | 2.3437499999 | 2.3437500000 | |
| ∗ 12 | 3 | 26 | 2.3399999999 | 2.3400000000 | |
| ∗ 12 | 3 | 27 | 2.3365384615 | 2.3365384616 | |
| ∗ 12 | 3 | 28 | 2.3333333333 | 2.3333333334 | |
| ∗ 12 | 3 | 29 | 2.3303571428 | 2.3303571429 | |
| ∗ 12 | 3 | 30 | 2.3275862068 | 2.3275862069 | |
| ∗ 12 | 3 | 31 | 2.3249999999 | 2.3250000000 | |
| ∗ 12 | 3 | 32 | 2.3225806451 | 2.3225806452 | |
| ∗ 12 | 3 | 33 | 2.3203124999 | 2.3203125000 | |
| ∗ 12 | 3 | 34 | 2.3181818181 | 2.3181818182 | |
| ∗ 12 | 3 | 35 | 2.3161764705 | 2.3161764706 | |
| ∗ 12 | 3 | 36 | 2.3142857142 | 2.3142857143 | |
| ∗ 12 | 3 | 37 | 2.3124999999 | 2.3125000000 | |
| ∗ 12 | 3 | 38 | 2.3108108108 | 2.3108108109 | |
| ∗ 12 | 3 | 39 | 2.3092105263 | 2.3092105264 | |
| ∗ 12 | 3 | 40 | 2.3076923076 | 2.3076923077 | |
| ∗ 12 | 3 | 41 | 2.3062499999 | 2.3062500000 | |
| ∗ 12 | 3 | 42 | 2.3048780487 | 2.3048780488 | |
| ∗ 12 | 3 | 43 | 2.3035714285 | 2.3035714286 | |
| ∗ 12 | 3 | 44 | 2.3023255813 | 2.3023255814 | |
| ∗ 12 | 3 | 45 | 2.3011363636 | 2.3011363637 | |
| ∗ 12 | 3 | 46 | 2.2999999999 | 2.3000000000 | |
| ∗ 12 | 3 | 47 | 2.2989130434 | 2.2989130435 | |
| ∗ 12 | 3 | 48 | 2.2978723404 | 2.2978723405 | |
| ∗ 12 | 3 | 49 | 2.2968749999 | 2.2968750000 | |
| ∗ 12 | 3 | 50 | 2.2959183673 | 2.2959183674 | |
| 12 | 3 | 51 | 2.2949991496 | 2.2950000000 | |
| 12 | 3 | 52 | 2.2940625934 | 2.2941176471 | |
| 12 | 3 | 53 | 2.2929952316 | 2.2932692308 | |
| 12 | 3 | 54 | 2.2917458017 | 2.2924528302 | |
| 12 | 3 | 55 | 2.2905900848 | 2.2916666667 | |
| 12 | 3 | 56 | 2.2893490359 | 2.2909090910 | |
| 12 | 3 | 57 | 2.2879824291 | 2.2901785715 | |
| 12 | 3 | 58 | 2.2865745896 | 2.2894736843 | |
| 12 | 3 | 59 | 2.2852701943 | 2.2887931035 | |
| 12 | 3 | 60 | 2.2837895210 | 2.2881355933 | |
| 12 | 3 | 61 | 2.2821930183 | 2.2875000000 | |
| 12 | 3 | 62 | 2.2807862765 | 2.2868852460 | |
| 12 | 3 | 63 | 2.2792252242 | 2.2862903226 | |
| 12 | 3 | 64 | 2.2779111398 | 2.2857142858 | |
| 12 | 3 | 65 | 2.2762164378 | 2.2851562500 | |
| 12 | 3 | 66 | 2.2745035234 | 2.2846153847 | |
| 12 | 3 | 67 | 2.2728778938 | 2.2840909091 | |
| 12 | 3 | 68 | 2.2713810499 | 2.2835820896 | |
| 12 | 3 | 69 | 2.2696516590 | 2.2830882353 | |
| 12 | 3 | 70 | 2.2684255439 | 2.2826086957 | |
| 12 | 3 | 71 | 2.2665738629 | 2.2821428572 | |
| 12 | 3 | 72 | 2.2647834950 | 2.2816901409 | |
| 12 | 3 | 73 | 2.2633100923 | 2.2812500000 | |
| 12 | 3 | 74 | 2.2617134461 | 2.2808219179 | |
| 12 | 3 | 75 | 2.2600573944 | 2.2804054055 | |
| 12 | 3 | 76 | 2.2581982518 | 2.2800000000 | |
| 12 | 3 | 77 | 2.2565024779 | 2.2796052632 | |
| 12 | 3 | 78 | 2.2548273749 | 2.2792207793 | |
| 12 | 3 | 79 | 2.2493061299 | 2.2500000000 | |
| 12 | 3 | 80 | 2.2440270228 | 2.2500000000 | |
| 12 | 3 | 81 | 2.2413810109 | 2.2500000000 | |
| 12 | 3 | 82 | 2.2381170918 | 2.2500000000 | |
| 12 | 3 | 83 | 2.2363252164 | 2.2500000000 | |
| 12 | 3 | 84 | 2.2327342283 | 2.2500000000 | |
| 12 | 3 | 85 | 2.2297930737 | 2.2500000000 | |
| 12 | 3 | 86 | 2.2273151274 | 2.2500000000 | |
| 12 | 3 | 87 | 2.2258962952 | 2.2500000000 | |
| 12 | 3 | 88 | 2.2243120636 | 2.2500000000 | |
| 12 | 3 | 89 | 2.2221158236 | 2.2500000000 | |
| 12 | 3 | 90 | 2.2199486582 | 2.2500000000 | |
| 12 | 3 | 91 | 2.2181139268 | 2.2500000000 | |
| 12 | 3 | 92 | 2.2161402375 | 2.2500000000 | |
| 12 | 3 | 93 | 2.2141106123 | 2.2500000000 | |
| 12 | 3 | 94 | 2.2120896590 | 2.2500000000 | |
| ∗ 12 | 4 | 50 | 2.7210884353 | 2.7210884354 | |
| ∗ 12 | 4 | 51 | 2.7199999999 | 2.7200000000 | |
| ∗ 12 | 4 | 52 | 2.7189542483 | 2.7189542484 | |
| ∗ 12 | 4 | 53 | 2.7179487179 | 2.7179487180 | |
| ∗ 12 | 4 | 54 | 2.7169811320 | 2.7169811321 | |
| ∗ 12 | 4 | 55 | 2.7160493827 | 2.7160493828 | |
| ∗ 12 | 4 | 56 | 2.7151515151 | 2.7151515152 | |
| ∗ 12 | 4 | 57 | 2.7142857142 | 2.7142857143 | |
| ∗ 12 | 4 | 58 | 2.7134502923 | 2.7134502924 | |
| ∗ 12 | 4 | 59 | 2.7126436781 | 2.7126436782 | |
| ∗ 12 | 4 | 60 | 2.7118644067 | 2.7118644068 | |
| 12 | 4 | 61 | 2.7111111104 | 2.7111111112 | unclear whether bound is tight |
| 12 | 4 | 62 | 2.7103812619 | 2.7103825137 | |
| 12 | 4 | 63 | 2.7095949171 | 2.7096774194 | |
| 12 | 4 | 64 | 2.7086459776 | 2.7089947090 | |
| 12 | 4 | 65 | 2.7076697320 | 2.7083333334 | |
| 12 | 4 | 66 | 2.7065884729 | 2.7076923077 | |
| 12 | 4 | 67 | 2.7054060876 | 2.7070707071 | |
| 12 | 4 | 68 | 2.7042085158 | 2.7064676617 | |
| 12 | 4 | 69 | 2.7028355785 | 2.7058823530 | |
| 12 | 4 | 70 | 2.7016879315 | 2.7053140097 | |
| 12 | 4 | 71 | 2.7002482462 | 2.7047619048 | |
| 12 | 4 | 72 | 2.6989605047 | 2.7042253522 | |
| 12 | 4 | 73 | 2.6976082395 | 2.7037037038 | |
| 12 | 4 | 74 | 2.6961342265 | 2.7031963471 | |
| 12 | 4 | 75 | 2.6946416490 | 2.7027027028 | |
| 12 | 4 | 76 | 2.6934515172 | 2.7022222223 | |
| 12 | 4 | 77 | 2.6918100770 | 2.7017543860 | |
| 12 | 4 | 78 | 2.6907870505 | 2.7012987013 | |
| ∗ 12 | 4 | 79 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 80 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 81 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 82 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 83 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 84 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 85 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 86 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 87 | 2.6666666666 | 2.6666666667 | |
| ∗ 12 | 4 | 88 | 2.6666666666 | 2.6666666667 | |
| 12 | 4 | 89 | 2.6648739869 | 2.6666666667 | |
| 12 | 4 | 90 | 2.6636723791 | 2.6666666667 | |
| 12 | 4 | 91 | 2.6617069770 | 2.6666666667 | |
| 12 | 4 | 92 | 2.6595563998 | 2.6666666667 | |
| 12 | 4 | 93 | 2.6587892087 | 2.6666666667 | |
| 12 | 5 | 78 | 2.9504582094 | 2.9545454546 | |
| 12 | 6 | 78 | 3.0365665523 | 3.0389610390 | |
| ∗ 13 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 12 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 13 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 13 | 1 | 14 | 0.9940828402 | 0.9940828403 | tight bound |
| 13 | 1 | 15 | 0.9876543209 | 0.9890109891 | |
| 13 | 1 | 16 | 0.9817758633 | 0.9846153847 | |
| 13 | 1 | 17 | 0.9772809484 | 0.9807692308 | Henry Cohn, 2025 |
| 13 | 1 | 18 | 0.9747366327 | 0.9773755657 | |
| 13 | 1 | 19 | 0.9723517424 | 0.9743589744 | |
| 13 | 1 | 20 | 0.9686827440 | 0.9716599191 | |
| 13 | 1 | 21 | 0.9670166565 | 0.9692307693 | |
| 13 | 1 | 22 | 0.9648781362 | 0.9670329671 | |
| 13 | 1 | 23 | 0.9611207212 | 0.9650349651 | Henry Cohn, 2025 |
| 13 | 1 | 24 | 0.9600000052 | 0.9632107024 | Henry Cohn, 2025 |
| 13 | 1 | 25 | 0.9599999999 | 0.9615384616 | |
| ∗ 13 | 1 | 26 | 0.9599999999 | 0.9600000000 | tight bound |
| 13 | 1 | 27 | 0.9524355201 | 0.9585798817 | Henry Cohn, 2024 |
| 13 | 1 | 28 | 0.9514387655 | 0.9572649573 | Henry Cohn, 2024 |
| 13 | 1 | 29 | 0.9488978326 | 0.9560439561 | Henry Cohn, 2025 |
| 13 | 1 | 30 | 0.9471652344 | 0.9549071619 | Henry Cohn, 2025 |
| 13 | 1 | 31 | 0.9462830884 | 0.9538461539 | Henry Cohn, 2024 |
| 13 | 1 | 32 | 0.9454405335 | 0.9528535981 | Henry Cohn, 2025 |
| 13 | 1 | 33 | 0.9432815871 | 0.9519230770 | Henry Cohn, 2024 |
| 13 | 1 | 34 | 0.9427605244 | 0.9510489511 | Henry Cohn, 2025 |
| 13 | 1 | 35 | 0.9420863940 | 0.9502262444 | |
| 13 | 1 | 36 | 0.9410233703 | 0.9494505495 | Henry Cohn, 2025 |
| 13 | 1 | 37 | 0.9396422979 | 0.9487179488 | Henry Cohn, 2025 |
| 13 | 1 | 38 | 0.9381713027 | 0.9480249481 | |
| 13 | 1 | 39 | 0.9375783955 | 0.9473684211 | Henry Cohn, 2025 |
| 13 | 1 | 40 | 0.9375389008 | 0.9467455622 | Henry Cohn, 2025 |
| 13 | 1 | 41 | 0.9375034937 | 0.9461538462 | |
| 13 | 1 | 42 | 0.9375007580 | 0.9455909944 | Henry Cohn, 2025 |
| 13 | 1 | 43 | 0.9375000000 | 0.9450549451 | |
| 13 | 1 | 44 | 0.9375000000 | 0.9445438283 | |
| 13 | 1 | 45 | 0.9375000000 | 0.9440559441 | |
| 13 | 1 | 46 | 0.9375000000 | 0.9435897436 | |
| 13 | 1 | 47 | 0.9375000000 | 0.9431438128 | |
| 13 | 1 | 48 | 0.9375000000 | 0.9427168577 | |
| 13 | 1 | 49 | 0.9375000000 | 0.9423076924 | |
| 13 | 1 | 50 | 0.9375000000 | 0.9419152277 | |
| 13 | 1 | 51 | 0.9375000000 | 0.9415384616 | |
| 13 | 1 | 52 | 0.9375000000 | 0.9411764706 | |
| 13 | 1 | 53 | 0.9292977154 | 0.9408284024 | Henry Cohn, 2025 |
| 13 | 1 | 54 | 0.9222658555 | 0.9404934688 | |
| 13 | 1 | 91 | 0.8907672709 | 0.9333333334 | |
| ∗ 13 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 13 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 13 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 13 | 2 | 6 | 1.9999999999 | 2.0000000000 | tight bound |
| 13 | 2 | 7 | 1.9722222222 | 1.9743589744 | |
| 13 | 2 | 8 | 1.9337352840 | 1.9340659341 | |
| ∗ 13 | 2 | 9 | 1.9038461538 | 1.9038461539 | |
| ∗ 13 | 2 | 10 | 1.8803418803 | 1.8803418804 | |
| ∗ 13 | 2 | 11 | 1.8615384615 | 1.8615384616 | |
| ∗ 13 | 2 | 12 | 1.8461538461 | 1.8461538462 | |
| ∗ 13 | 2 | 13 | 1.8333333333 | 1.8333333334 | |
| ∗ 13 | 2 | 14 | 1.8224852071 | 1.8224852072 | |
| ∗ 13 | 2 | 15 | 1.8131868131 | 1.8131868132 | |
| ∗ 13 | 2 | 16 | 1.8051282051 | 1.8051282052 | |
| ∗ 13 | 2 | 17 | 1.7980769230 | 1.7980769231 | |
| ∗ 13 | 2 | 18 | 1.7918552036 | 1.7918552037 | |
| ∗ 13 | 2 | 19 | 1.7863247863 | 1.7863247864 | |
| ∗ 13 | 2 | 20 | 1.7813765182 | 1.7813765183 | |
| ∗ 13 | 2 | 21 | 1.7769230769 | 1.7769230770 | |
| ∗ 13 | 2 | 22 | 1.7728937728 | 1.7728937729 | |
| ∗ 13 | 2 | 23 | 1.7692307692 | 1.7692307693 | |
| ∗ 13 | 2 | 24 | 1.7658862876 | 1.7658862877 | |
| ∗ 13 | 2 | 25 | 1.7628205128 | 1.7628205129 | |
| ∗ 13 | 2 | 26 | 1.7599999999 | 1.7600000000 | |
| ∗ 13 | 2 | 27 | 1.7573964497 | 1.7573964498 | |
| ∗ 13 | 2 | 28 | 1.7549857549 | 1.7549857550 | |
| ∗ 13 | 2 | 29 | 1.7527472527 | 1.7527472528 | |
| ∗ 13 | 2 | 30 | 1.7506631299 | 1.7506631300 | |
| ∗ 13 | 2 | 31 | 1.7487179487 | 1.7487179488 | |
| ∗ 13 | 2 | 32 | 1.7468982630 | 1.7468982631 | |
| ∗ 13 | 2 | 33 | 1.7451923076 | 1.7451923077 | |
| ∗ 13 | 2 | 34 | 1.7435897435 | 1.7435897436 | |
| ∗ 13 | 2 | 35 | 1.7420814479 | 1.7420814480 | |
| ∗ 13 | 2 | 36 | 1.7406593406 | 1.7406593407 | |
| ∗ 13 | 2 | 37 | 1.7393162393 | 1.7393162394 | |
| ∗ 13 | 2 | 38 | 1.7380457380 | 1.7380457381 | |
| ∗ 13 | 2 | 39 | 1.7368421052 | 1.7368421053 | |
| 13 | 2 | 40 | 1.7356996512 | 1.7357001973 | |
| 13 | 2 | 41 | 1.7344806530 | 1.7346153847 | |
| 13 | 2 | 42 | 1.7332084018 | 1.7335834897 | |
| 13 | 2 | 43 | 1.7318682917 | 1.7326007327 | |
| 13 | 2 | 44 | 1.7304271306 | 1.7316636852 | |
| 13 | 2 | 45 | 1.7290343294 | 1.7307692308 | |
| 13 | 2 | 46 | 1.7276352001 | 1.7299145300 | |
| 13 | 2 | 47 | 1.7261182645 | 1.7290969900 | |
| 13 | 2 | 48 | 1.7252778365 | 1.7283142390 | |
| 13 | 2 | 49 | 1.7231403771 | 1.7275641026 | |
| 13 | 2 | 50 | 1.7217656705 | 1.7268445840 | |
| 13 | 2 | 52 | 1.7161977524 | 1.7254901961 | |
| 13 | 2 | 91 | 1.6596375077 | 1.7111111112 | |
| ∗ 13 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 13 | 3 | 4 | 2.9999999999 | 3.0000000000 | tight bound |
| 13 | 3 | 5 | 2.8749999999 | 2.8846153847 | |
| 13 | 3 | 6 | 2.7692307690 | 2.7692307693 | unclear whether bound is tight |
| ∗ 13 | 3 | 7 | 2.6923076923 | 2.6923076924 | |
| ∗ 13 | 3 | 8 | 2.6373626373 | 2.6373626374 | |
| ∗ 13 | 3 | 9 | 2.5961538461 | 2.5961538462 | |
| ∗ 13 | 3 | 10 | 2.5641025641 | 2.5641025642 | |
| ∗ 13 | 3 | 11 | 2.5384615384 | 2.5384615385 | |
| ∗ 13 | 3 | 12 | 2.5174825174 | 2.5174825175 | |
| ∗ 13 | 3 | 13 | 2.4999999999 | 2.5000000000 | |
| ∗ 13 | 3 | 14 | 2.4852071005 | 2.4852071006 | |
| ∗ 13 | 3 | 15 | 2.4725274725 | 2.4725274726 | |
| ∗ 13 | 3 | 16 | 2.4615384615 | 2.4615384616 | |
| ∗ 13 | 3 | 17 | 2.4519230769 | 2.4519230770 | |
| ∗ 13 | 3 | 18 | 2.4434389140 | 2.4434389141 | |
| ∗ 13 | 3 | 19 | 2.4358974358 | 2.4358974359 | |
| ∗ 13 | 3 | 20 | 2.4291497975 | 2.4291497976 | |
| ∗ 13 | 3 | 21 | 2.4230769230 | 2.4230769231 | |
| ∗ 13 | 3 | 22 | 2.4175824175 | 2.4175824176 | |
| ∗ 13 | 3 | 23 | 2.4125874125 | 2.4125874126 | |
| ∗ 13 | 3 | 24 | 2.4080267558 | 2.4080267559 | |
| ∗ 13 | 3 | 25 | 2.4038461538 | 2.4038461539 | |
| ∗ 13 | 3 | 26 | 2.3999999999 | 2.4000000000 | |
| ∗ 13 | 3 | 27 | 2.3964497041 | 2.3964497042 | |
| ∗ 13 | 3 | 28 | 2.3931623931 | 2.3931623932 | |
| ∗ 13 | 3 | 29 | 2.3901098901 | 2.3901098902 | |
| ∗ 13 | 3 | 30 | 2.3872679045 | 2.3872679046 | |
| ∗ 13 | 3 | 31 | 2.3846153846 | 2.3846153847 | |
| ∗ 13 | 3 | 32 | 2.3821339950 | 2.3821339951 | |
| ∗ 13 | 3 | 33 | 2.3798076923 | 2.3798076924 | |
| ∗ 13 | 3 | 34 | 2.3776223776 | 2.3776223777 | |
| ∗ 13 | 3 | 35 | 2.3755656108 | 2.3755656109 | |
| ∗ 13 | 3 | 36 | 2.3736263736 | 2.3736263737 | |
| ∗ 13 | 3 | 37 | 2.3717948717 | 2.3717948718 | |
| ∗ 13 | 3 | 38 | 2.3700623700 | 2.3700623701 | |
| ∗ 13 | 3 | 39 | 2.3684210526 | 2.3684210527 | |
| ∗ 13 | 3 | 40 | 2.3668639053 | 2.3668639054 | |
| ∗ 13 | 3 | 41 | 2.3653846153 | 2.3653846154 | |
| ∗ 13 | 3 | 42 | 2.3639774859 | 2.3639774860 | |
| ∗ 13 | 3 | 43 | 2.3626373626 | 2.3626373627 | |
| ∗ 13 | 3 | 44 | 2.3613595706 | 2.3613595707 | |
| ∗ 13 | 3 | 45 | 2.3601398601 | 2.3601398602 | |
| ∗ 13 | 3 | 46 | 2.3589743589 | 2.3589743590 | |
| ∗ 13 | 3 | 47 | 2.3578595317 | 2.3578595318 | |
| ∗ 13 | 3 | 48 | 2.3567921440 | 2.3567921441 | |
| ∗ 13 | 3 | 49 | 2.3557692307 | 2.3557692308 | |
| ∗ 13 | 3 | 50 | 2.3547880690 | 2.3547880691 | |
| ∗ 13 | 3 | 52 | 2.3529411764 | 2.3529411765 | |
| 13 | 3 | 65 | 2.3392699537 | 2.3437500000 | |
| 13 | 3 | 91 | 2.3055384814 | 2.3333333334 | |
| 13 | 4 | 91 | 2.7872406035 | 2.8000000000 | |
| 13 | 5 | 91 | 3.1058033700 | 3.1111111112 | |
| 13 | 5 | 92 | 3.0769111008 | 3.0769230770 | |
| 13 | 6 | 91 | 3.2644910682 | 3.2666666667 | |
| ∗ 14 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 12 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 13 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 14 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 14 | 1 | 15 | 0.9948979591 | 0.9948979592 | tight bound |
| 14 | 1 | 16 | 0.9886719278 | 0.9904761905 | |
| 14 | 1 | 17 | 0.9840783026 | 0.9866071429 | Henry Cohn, 2023 |
| 14 | 1 | 18 | 0.9802977940 | 0.9831932774 | |
| 14 | 1 | 19 | 0.9771711613 | 0.9801587302 | Henry Cohn, 2025 |
| 14 | 1 | 20 | 0.9752088818 | 0.9774436091 | |
| 14 | 1 | 21 | 0.9720844560 | 0.9750000000 | Henry Cohn, 2024 |
| 14 | 1 | 22 | 0.9699345991 | 0.9727891157 | Henry Cohn, 2025 |
| 14 | 1 | 23 | 0.9682592472 | 0.9707792208 | Henry Cohn, 2024 |
| 14 | 1 | 24 | 0.9666046313 | 0.9689440994 | |
| 14 | 1 | 25 | 0.9637601368 | 0.9672619048 | Henry Cohn, 2024 |
| 14 | 1 | 26 | 0.9616651911 | 0.9657142858 | Henry Cohn, 2025 |
| 14 | 1 | 27 | 0.9604604341 | 0.9642857143 | Henry Cohn, 2024 |
| 14 | 1 | 28 | 0.9600109385 | 0.9629629630 | Henry Cohn, 2025 |
| 14 | 1 | 29 | 0.9562518613 | 0.9617346939 | Henry Cohn, 2025 |
| 14 | 1 | 30 | 0.9544511977 | 0.9605911331 | Henry Cohn, 2024 |
| 14 | 1 | 31 | 0.9528465226 | 0.9595238096 | Henry Cohn, 2024 |
| 14 | 1 | 32 | 0.9514979997 | 0.9585253457 | Henry Cohn, 2024 |
| 14 | 1 | 33 | 0.9500994466 | 0.9575892858 | Henry Cohn, 2025 |
| 14 | 1 | 34 | 0.9484643770 | 0.9567099568 | Henry Cohn, 2024 |
| 14 | 1 | 35 | 0.9470784054 | 0.9558823530 | Henry Cohn, 2024 |
| 14 | 1 | 36 | 0.9456740447 | 0.9551020409 | Henry Cohn, 2024 |
| 14 | 1 | 37 | 0.9443326259 | 0.9543650794 | Henry Cohn, 2024 |
| 14 | 1 | 38 | 0.9430659148 | 0.9536679537 | Henry Cohn, 2025 |
| 14 | 1 | 39 | 0.9417034512 | 0.9530075188 | Henry Cohn, 2025 |
| 14 | 1 | 40 | 0.9407044671 | 0.9523809524 | Henry Cohn, 2025 |
| 14 | 1 | 41 | 0.9401766934 | 0.9517857143 | Henry Cohn, 2025 |
| 14 | 1 | 42 | 0.9394805773 | 0.9512195122 | Henry Cohn, 2025 |
| 14 | 1 | 43 | 0.9388887623 | 0.9506802722 | Henry Cohn, 2025 |
| 14 | 1 | 44 | 0.9382483304 | 0.9501661130 | Henry Cohn, 2025 |
| 14 | 1 | 45 | 0.9380169523 | 0.9496753247 | Henry Cohn, 2025 |
| 14 | 1 | 46 | 0.9379243726 | 0.9492063493 | Henry Cohn, 2025 |
| 14 | 1 | 47 | 0.9379061045 | 0.9487577640 | |
| 14 | 1 | 48 | 0.9377179685 | 0.9483282675 | Henry Cohn, 2025 |
| 14 | 1 | 49 | 0.9376866827 | 0.9479166667 | |
| 14 | 1 | 50 | 0.9376866827 | 0.9475218659 | |
| 14 | 1 | 51 | 0.9375262731 | 0.9471428572 | |
| 14 | 1 | 52 | 0.9374999999 | 0.9467787115 | |
| 14 | 1 | 53 | 0.9374999998 | 0.9464285715 | |
| 14 | 1 | 54 | 0.9374999998 | 0.9460916443 | |
| 14 | 1 | 55 | 0.9374876074 | 0.9457671958 | |
| 14 | 1 | 65 | 0.9198475615 | 0.9430803572 | Henry Cohn, 2025 |
| ∗ 14 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 14 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 14 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 14 | 2 | 6 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 14 | 2 | 7 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 14 | 2 | 8 | 1.9591836734 | 1.9591836735 | |
| 14 | 2 | 9 | 1.9285711819 | 1.9285714286 | |
| ∗ 14 | 2 | 10 | 1.9047619047 | 1.9047619048 | |
| ∗ 14 | 2 | 11 | 1.8857142857 | 1.8857142858 | |
| ∗ 14 | 2 | 12 | 1.8701298701 | 1.8701298702 | |
| ∗ 14 | 2 | 13 | 1.8571428571 | 1.8571428572 | |
| ∗ 14 | 2 | 14 | 1.8461538461 | 1.8461538462 | |
| ∗ 14 | 2 | 15 | 1.8367346938 | 1.8367346939 | |
| ∗ 14 | 2 | 16 | 1.8285714285 | 1.8285714286 | |
| ∗ 14 | 2 | 17 | 1.8214285714 | 1.8214285715 | |
| ∗ 14 | 2 | 18 | 1.8151260504 | 1.8151260505 | |
| ∗ 14 | 2 | 19 | 1.8095238095 | 1.8095238096 | |
| ∗ 14 | 2 | 20 | 1.8045112781 | 1.8045112782 | |
| ∗ 14 | 2 | 21 | 1.7999999999 | 1.8000000000 | |
| ∗ 14 | 2 | 22 | 1.7959183673 | 1.7959183674 | |
| ∗ 14 | 2 | 23 | 1.7922077922 | 1.7922077923 | |
| ∗ 14 | 2 | 24 | 1.7888198757 | 1.7888198758 | |
| ∗ 14 | 2 | 25 | 1.7857142857 | 1.7857142858 | |
| ∗ 14 | 2 | 26 | 1.7828571428 | 1.7828571429 | |
| ∗ 14 | 2 | 27 | 1.7802197802 | 1.7802197803 | |
| ∗ 14 | 2 | 28 | 1.7777777777 | 1.7777777778 | |
| ∗ 14 | 2 | 29 | 1.7755102040 | 1.7755102041 | |
| ∗ 14 | 2 | 30 | 1.7733990147 | 1.7733990148 | |
| ∗ 14 | 2 | 31 | 1.7714285714 | 1.7714285715 | |
| ∗ 14 | 2 | 32 | 1.7695852534 | 1.7695852535 | |
| ∗ 14 | 2 | 33 | 1.7678571428 | 1.7678571429 | |
| ∗ 14 | 2 | 34 | 1.7662337662 | 1.7662337663 | |
| ∗ 14 | 2 | 35 | 1.7647058823 | 1.7647058824 | |
| ∗ 14 | 2 | 36 | 1.7632653061 | 1.7632653062 | |
| ∗ 14 | 2 | 37 | 1.7619047619 | 1.7619047620 | |
| ∗ 14 | 2 | 38 | 1.7606177606 | 1.7606177607 | |
| ∗ 14 | 2 | 39 | 1.7593984962 | 1.7593984963 | |
| ∗ 14 | 2 | 40 | 1.7582417582 | 1.7582417583 | |
| ∗ 14 | 2 | 41 | 1.7571428571 | 1.7571428572 | |
| ∗ 14 | 2 | 42 | 1.7560975609 | 1.7560975610 | |
| 14 | 2 | 43 | 1.7550911899 | 1.7551020409 | |
| 14 | 2 | 44 | 1.7540989947 | 1.7541528240 | |
| 14 | 2 | 45 | 1.7530591337 | 1.7532467533 | |
| 14 | 2 | 46 | 1.7519293994 | 1.7523809524 | |
| 14 | 2 | 47 | 1.7507975770 | 1.7515527951 | |
| 14 | 2 | 48 | 1.7495978826 | 1.7507598785 | |
| 14 | 2 | 49 | 1.7490705842 | 1.7500000000 | |
| 14 | 2 | 50 | 1.7471917410 | 1.7492711371 | |
| 14 | 2 | 56 | 1.7393235752 | 1.7454545455 | |
| ∗ 14 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 14 | 3 | 4 | 2.9999999999 | 3.0000000000 | tight bound |
| 14 | 3 | 5 | 2.9374999999 | 2.9464285715 | |
| 14 | 3 | 6 | 2.8285412523 | 2.8285714286 | |
| ∗ 14 | 3 | 7 | 2.7499999999 | 2.7500000000 | |
| ∗ 14 | 3 | 8 | 2.6938775510 | 2.6938775511 | |
| ∗ 14 | 3 | 9 | 2.6517857142 | 2.6517857143 | |
| ∗ 14 | 3 | 10 | 2.6190476190 | 2.6190476191 | |
| ∗ 14 | 3 | 11 | 2.5928571428 | 2.5928571429 | |
| ∗ 14 | 3 | 12 | 2.5714285714 | 2.5714285715 | |
| ∗ 14 | 3 | 13 | 2.5535714285 | 2.5535714286 | |
| ∗ 14 | 3 | 14 | 2.5384615384 | 2.5384615385 | |
| ∗ 14 | 3 | 15 | 2.5255102040 | 2.5255102041 | |
| ∗ 14 | 3 | 16 | 2.5142857142 | 2.5142857143 | |
| ∗ 14 | 3 | 17 | 2.5044642857 | 2.5044642858 | |
| ∗ 14 | 3 | 18 | 2.4957983193 | 2.4957983194 | |
| ∗ 14 | 3 | 19 | 2.4880952380 | 2.4880952381 | |
| ∗ 14 | 3 | 20 | 2.4812030075 | 2.4812030076 | |
| ∗ 14 | 3 | 21 | 2.4749999999 | 2.4750000000 | |
| ∗ 14 | 3 | 22 | 2.4693877551 | 2.4693877552 | |
| ∗ 14 | 3 | 23 | 2.4642857142 | 2.4642857143 | |
| ∗ 14 | 3 | 24 | 2.4596273291 | 2.4596273292 | |
| ∗ 14 | 3 | 25 | 2.4553571428 | 2.4553571429 | |
| ∗ 14 | 3 | 26 | 2.4514285714 | 2.4514285715 | |
| ∗ 14 | 3 | 27 | 2.4478021978 | 2.4478021979 | |
| ∗ 14 | 3 | 28 | 2.4444444444 | 2.4444444445 | |
| ∗ 14 | 3 | 29 | 2.4413265306 | 2.4413265307 | |
| ∗ 14 | 3 | 30 | 2.4384236453 | 2.4384236454 | |
| ∗ 14 | 3 | 31 | 2.4357142857 | 2.4357142858 | |
| ∗ 14 | 3 | 32 | 2.4331797235 | 2.4331797236 | |
| ∗ 14 | 3 | 33 | 2.4308035714 | 2.4308035715 | |
| ∗ 14 | 3 | 34 | 2.4285714285 | 2.4285714286 | |
| ∗ 14 | 3 | 35 | 2.4264705882 | 2.4264705883 | |
| ∗ 14 | 3 | 36 | 2.4244897959 | 2.4244897960 | |
| ∗ 14 | 3 | 37 | 2.4226190476 | 2.4226190477 | |
| ∗ 14 | 3 | 38 | 2.4208494208 | 2.4208494209 | |
| ∗ 14 | 3 | 39 | 2.4191729323 | 2.4191729324 | |
| ∗ 14 | 3 | 40 | 2.4175824175 | 2.4175824176 | |
| ∗ 14 | 3 | 41 | 2.4160714285 | 2.4160714286 | |
| ∗ 14 | 3 | 42 | 2.4146341463 | 2.4146341464 | |
| ∗ 14 | 3 | 43 | 2.4132653061 | 2.4132653062 | |
| ∗ 14 | 3 | 44 | 2.4119601328 | 2.4119601329 | |
| ∗ 14 | 3 | 45 | 2.4107142857 | 2.4107142858 | |
| ∗ 14 | 3 | 46 | 2.4095238095 | 2.4095238096 | |
| ∗ 14 | 3 | 47 | 2.4083850931 | 2.4083850932 | |
| ∗ 14 | 3 | 48 | 2.4072948328 | 2.4072948329 | |
| ∗ 14 | 3 | 49 | 2.4062499999 | 2.4062500000 | |
| ∗ 14 | 3 | 50 | 2.4052478134 | 2.4052478135 | |
| ∗ 14 | 3 | 56 | 2.3999999999 | 2.4000000000 | |
| 14 | 3 | 70 | 2.3881194065 | 2.3913043479 | |
| ∗ 15 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 12 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 13 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 14 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 15 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 15 | 1 | 16 | 0.9955555555 | 0.9955555556 | tight bound |
| 15 | 1 | 17 | 0.9902481956 | 0.9916666667 | Henry Cohn, 2025 |
| 15 | 1 | 18 | 0.9868130968 | 0.9882352942 | |
| 15 | 1 | 19 | 0.9826287206 | 0.9851851852 | Henry Cohn, 2025 |
| 15 | 1 | 20 | 0.9798365475 | 0.9824561404 | Henry Cohn, 2025 |
| 15 | 1 | 21 | 0.9795918367 | 0.9800000000 | |
| 15 | 1 | 22 | 0.9760677434 | 0.9777777778 | |
| 15 | 1 | 23 | 0.9734967714 | 0.9757575758 | |
| 15 | 1 | 24 | 0.9719034575 | 0.9739130435 | Henry Cohn, 2024 |
| 15 | 1 | 25 | 0.9698180096 | 0.9722222223 | |
| 15 | 1 | 26 | 0.9675054613 | 0.9706666667 | |
| 15 | 1 | 27 | 0.9658280494 | 0.9692307693 | Henry Cohn, 2024 |
| 15 | 1 | 28 | 0.9638514407 | 0.9679012346 | Henry Cohn, 2024 |
| 15 | 1 | 29 | 0.9622932472 | 0.9666666667 | Henry Cohn, 2024 |
| 15 | 1 | 30 | 0.9606843728 | 0.9655172414 | Henry Cohn, 2025 |
| 15 | 1 | 31 | 0.9591676069 | 0.9644444445 | Henry Cohn, 2024 |
| 15 | 1 | 32 | 0.9577699803 | 0.9634408603 | Henry Cohn, 2025 |
| 15 | 1 | 33 | 0.9563658940 | 0.9625000000 | Henry Cohn, 2024 |
| 15 | 1 | 34 | 0.9549891750 | 0.9616161617 | Henry Cohn, 2025 |
| 15 | 1 | 35 | 0.9537565866 | 0.9607843138 | Henry Cohn, 2024 |
| 15 | 1 | 36 | 0.9525841002 | 0.9600000000 | Henry Cohn, 2025 |
| 15 | 1 | 37 | 0.9512903014 | 0.9592592593 | Henry Cohn, 2024 |
| 15 | 1 | 38 | 0.9501564771 | 0.9585585586 | Henry Cohn, 2025 |
| 15 | 1 | 39 | 0.9490703759 | 0.9578947369 | Henry Cohn, 2025 |
| 15 | 1 | 40 | 0.9477566213 | 0.9572649573 | Henry Cohn, 2025 |
| 15 | 1 | 41 | 0.9466636432 | 0.9566666667 | Henry Cohn, 2024 |
| 15 | 1 | 42 | 0.9456153555 | 0.9560975610 | Henry Cohn, 2025 |
| 15 | 1 | 43 | 0.9445759622 | 0.9555555556 | Henry Cohn, 2025 |
| 15 | 1 | 44 | 0.9435117190 | 0.9550387597 | |
| 15 | 1 | 45 | 0.9426928860 | 0.9545454546 | Henry Cohn, 2025 |
| 15 | 1 | 46 | 0.9414551949 | 0.9540740741 | Henry Cohn, 2025 |
| 15 | 1 | 47 | 0.9405659944 | 0.9536231885 | Henry Cohn, 2025 |
| 15 | 1 | 48 | 0.9397109210 | 0.9531914894 | Henry Cohn, 2025 |
| 15 | 1 | 49 | 0.9388594788 | 0.9527777778 | |
| 15 | 1 | 50 | 0.9379233901 | 0.9523809524 | Henry Cohn, 2024 |
| ∗ 15 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 15 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 15 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 15 | 2 | 6 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 15 | 2 | 7 | 1.9999999999 | 2.0000000000 | tight bound |
| 15 | 2 | 8 | 1.9795918367 | 1.9809523810 | |
| 15 | 2 | 9 | 1.9497025614 | 1.9500000000 | |
| ∗ 15 | 2 | 10 | 1.9259259259 | 1.9259259260 | |
| ∗ 15 | 2 | 11 | 1.9066666666 | 1.9066666667 | |
| ∗ 15 | 2 | 12 | 1.8909090909 | 1.8909090910 | |
| ∗ 15 | 2 | 13 | 1.8777777777 | 1.8777777778 | |
| ∗ 15 | 2 | 14 | 1.8666666666 | 1.8666666667 | |
| ∗ 15 | 2 | 15 | 1.8571428571 | 1.8571428572 | |
| ∗ 15 | 2 | 16 | 1.8488888888 | 1.8488888889 | |
| ∗ 15 | 2 | 17 | 1.8416666666 | 1.8416666667 | |
| ∗ 15 | 2 | 18 | 1.8352941176 | 1.8352941177 | |
| ∗ 15 | 2 | 19 | 1.8296296296 | 1.8296296297 | |
| ∗ 15 | 2 | 20 | 1.8245614035 | 1.8245614036 | |
| ∗ 15 | 2 | 21 | 1.8199999999 | 1.8200000000 | |
| ∗ 15 | 2 | 22 | 1.8158730158 | 1.8158730159 | |
| ∗ 15 | 2 | 23 | 1.8121212121 | 1.8121212122 | |
| ∗ 15 | 2 | 24 | 1.8086956521 | 1.8086956522 | |
| ∗ 15 | 2 | 25 | 1.8055555555 | 1.8055555556 | |
| ∗ 15 | 2 | 26 | 1.8026666666 | 1.8026666667 | |
| ∗ 15 | 2 | 27 | 1.7999999999 | 1.8000000000 | |
| ∗ 15 | 2 | 28 | 1.7975308641 | 1.7975308642 | |
| ∗ 15 | 2 | 29 | 1.7952380952 | 1.7952380953 | |
| ∗ 15 | 2 | 30 | 1.7931034482 | 1.7931034483 | |
| ∗ 15 | 2 | 31 | 1.7911111111 | 1.7911111112 | |
| ∗ 15 | 2 | 32 | 1.7892473118 | 1.7892473119 | |
| ∗ 15 | 2 | 33 | 1.7874999999 | 1.7875000000 | |
| ∗ 15 | 2 | 34 | 1.7858585858 | 1.7858585859 | |
| ∗ 15 | 2 | 35 | 1.7843137254 | 1.7843137255 | |
| ∗ 15 | 2 | 36 | 1.7828571428 | 1.7828571429 | |
| ∗ 15 | 2 | 37 | 1.7814814814 | 1.7814814815 | |
| ∗ 15 | 2 | 38 | 1.7801801801 | 1.7801801802 | |
| ∗ 15 | 2 | 39 | 1.7789473684 | 1.7789473685 | |
| ∗ 15 | 2 | 40 | 1.7777777777 | 1.7777777778 | |
| ∗ 15 | 2 | 41 | 1.7766666666 | 1.7766666667 | |
| ∗ 15 | 2 | 42 | 1.7756097560 | 1.7756097561 | |
| ∗ 15 | 2 | 43 | 1.7746031746 | 1.7746031747 | |
| ∗ 15 | 2 | 44 | 1.7736434108 | 1.7736434109 | |
| ∗ 15 | 2 | 45 | 1.7727272727 | 1.7727272728 | |
| 15 | 2 | 46 | 1.7718518263 | 1.7718518519 | unclear whether bound is tight |
| 15 | 2 | 47 | 1.7709980945 | 1.7710144928 | |
| 15 | 2 | 48 | 1.7701248214 | 1.7702127660 | |
| 15 | 2 | 49 | 1.7692215240 | 1.7694444445 | |
| 15 | 2 | 50 | 1.7682317597 | 1.7687074830 | |
| 15 | 2 | 60 | 1.7574728085 | 1.7627118645 | |
| ∗ 15 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 15 | 3 | 4 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 15 | 3 | 5 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 15 | 3 | 6 | 2.8799999999 | 2.8800000000 | |
| ∗ 15 | 3 | 7 | 2.7999999999 | 2.8000000000 | |
| ∗ 15 | 3 | 8 | 2.7428571428 | 2.7428571429 | |
| ∗ 15 | 3 | 9 | 2.6999999999 | 2.7000000000 | |
| ∗ 15 | 3 | 10 | 2.6666666666 | 2.6666666667 | |
| ∗ 15 | 3 | 11 | 2.6399999999 | 2.6400000000 | |
| ∗ 15 | 3 | 12 | 2.6181818181 | 2.6181818182 | |
| ∗ 15 | 3 | 13 | 2.5999999999 | 2.6000000000 | |
| ∗ 15 | 3 | 14 | 2.5846153846 | 2.5846153847 | |
| ∗ 15 | 3 | 15 | 2.5714285714 | 2.5714285715 | |
| ∗ 15 | 3 | 16 | 2.5599999999 | 2.5600000000 | |
| ∗ 15 | 3 | 17 | 2.5499999999 | 2.5500000000 | |
| ∗ 15 | 3 | 18 | 2.5411764705 | 2.5411764706 | |
| ∗ 15 | 3 | 19 | 2.5333333333 | 2.5333333334 | |
| ∗ 15 | 3 | 20 | 2.5263157894 | 2.5263157895 | |
| ∗ 15 | 3 | 21 | 2.5199999999 | 2.5200000000 | |
| ∗ 15 | 3 | 22 | 2.5142857142 | 2.5142857143 | |
| ∗ 15 | 3 | 23 | 2.5090909090 | 2.5090909091 | |
| ∗ 15 | 3 | 24 | 2.5043478260 | 2.5043478261 | |
| ∗ 15 | 3 | 25 | 2.4999999999 | 2.5000000000 | |
| ∗ 15 | 3 | 26 | 2.4959999999 | 2.4960000000 | |
| ∗ 15 | 3 | 27 | 2.4923076923 | 2.4923076924 | |
| ∗ 15 | 3 | 28 | 2.4888888888 | 2.4888888889 | |
| ∗ 15 | 3 | 29 | 2.4857142857 | 2.4857142858 | |
| ∗ 15 | 3 | 30 | 2.4827586206 | 2.4827586207 | |
| ∗ 15 | 3 | 31 | 2.4799999999 | 2.4800000000 | |
| ∗ 15 | 3 | 32 | 2.4774193548 | 2.4774193549 | |
| ∗ 15 | 3 | 33 | 2.4749999999 | 2.4750000000 | |
| ∗ 15 | 3 | 34 | 2.4727272727 | 2.4727272728 | |
| ∗ 15 | 3 | 35 | 2.4705882352 | 2.4705882353 | |
| ∗ 15 | 3 | 36 | 2.4685714285 | 2.4685714286 | |
| ∗ 15 | 3 | 37 | 2.4666666666 | 2.4666666667 | |
| ∗ 15 | 3 | 38 | 2.4648648648 | 2.4648648649 | |
| ∗ 15 | 3 | 39 | 2.4631578947 | 2.4631578948 | |
| ∗ 15 | 3 | 40 | 2.4615384615 | 2.4615384616 | |
| ∗ 15 | 3 | 41 | 2.4599999999 | 2.4600000000 | |
| ∗ 15 | 3 | 42 | 2.4585365853 | 2.4585365854 | |
| ∗ 15 | 3 | 43 | 2.4571428571 | 2.4571428572 | |
| ∗ 15 | 3 | 44 | 2.4558139534 | 2.4558139535 | |
| ∗ 15 | 3 | 45 | 2.4545454545 | 2.4545454546 | |
| ∗ 15 | 3 | 46 | 2.4533333333 | 2.4533333334 | |
| ∗ 15 | 3 | 47 | 2.4521739130 | 2.4521739131 | |
| ∗ 15 | 3 | 48 | 2.4510638297 | 2.4510638298 | |
| ∗ 15 | 3 | 49 | 2.4499999999 | 2.4500000000 | |
| ∗ 15 | 3 | 50 | 2.4489795918 | 2.4489795919 | |
| ∗ 15 | 3 | 60 | 2.4406779661 | 2.4406779662 | |
| 15 | 3 | 75 | 2.4308855203 | 2.4324324325 | |
| ∗ 16 | 1 | 3 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 4 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 5 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 6 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 7 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 8 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 9 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 10 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 11 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 12 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 13 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 14 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 15 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 16 | 0.9999999999 | 1.0000000000 | tight bound |
| ∗ 16 | 1 | 17 | 0.9960937499 | 0.9960937500 | tight bound |
| 16 | 1 | 18 | 0.9917355371 | 0.9926470589 | |
| 16 | 1 | 19 | 0.9876376448 | 0.9895833334 | Henry Cohn, 2025 |
| 16 | 1 | 20 | 0.9850978821 | 0.9868421053 | |
| 16 | 1 | 21 | 0.9821412271 | 0.9843750000 | |
| 16 | 1 | 22 | 0.9808005969 | 0.9821428572 | |
| 16 | 1 | 23 | 0.9795918367 | 0.9801136364 | |
| 16 | 1 | 24 | 0.9761802947 | 0.9782608696 | |
| 16 | 1 | 25 | 0.9747366327 | 0.9765625000 | |
| 16 | 1 | 26 | 0.9734216394 | 0.9750000000 | Henry Cohn, 2025 |
| 16 | 1 | 27 | 0.9708073031 | 0.9735576924 | Henry Cohn, 2024 |
| 16 | 1 | 28 | 0.9691330913 | 0.9722222223 | Henry Cohn, 2025 |
| 16 | 1 | 29 | 0.9674988184 | 0.9709821429 | Henry Cohn, 2024 |
| 16 | 1 | 30 | 0.9660245892 | 0.9698275863 | Henry Cohn, 2024 |
| 16 | 1 | 31 | 0.9646698158 | 0.9687500000 | Henry Cohn, 2024 |
| 16 | 1 | 32 | 0.9632458817 | 0.9677419355 | Henry Cohn, 2024 |
| 16 | 1 | 33 | 0.9619854431 | 0.9667968750 | |
| 16 | 1 | 34 | 0.9606227333 | 0.9659090910 | Henry Cohn, 2025 |
| 16 | 1 | 35 | 0.9593839016 | 0.9650735295 | Henry Cohn, 2024 |
| 16 | 1 | 36 | 0.9582315556 | 0.9642857143 | Henry Cohn, 2024 |
| 16 | 1 | 37 | 0.9571169981 | 0.9635416667 | Henry Cohn, 2024 |
| 16 | 1 | 38 | 0.9559973612 | 0.9628378379 | Henry Cohn, 2024 |
| 16 | 1 | 39 | 0.9549591964 | 0.9621710527 | Henry Cohn, 2025 |
| 16 | 1 | 40 | 0.9539121117 | 0.9615384616 | Henry Cohn, 2025 |
| 16 | 1 | 41 | 0.9529470231 | 0.9609375000 | Henry Cohn, 2024 |
| 16 | 1 | 42 | 0.9519322657 | 0.9603658537 | Henry Cohn, 2024 |
| 16 | 1 | 43 | 0.9509257150 | 0.9598214286 | Henry Cohn, 2025 |
| 16 | 1 | 44 | 0.9499676937 | 0.9593023256 | Henry Cohn, 2025 |
| 16 | 1 | 45 | 0.9489907167 | 0.9588068182 | Henry Cohn, 2025 |
| 16 | 1 | 46 | 0.9480618859 | 0.9583333334 | Henry Cohn, 2025 |
| 16 | 1 | 47 | 0.9471223815 | 0.9578804348 | Henry Cohn, 2024 |
| 16 | 1 | 48 | 0.9461872031 | 0.9574468086 | Henry Cohn, 2025 |
| 16 | 1 | 49 | 0.9453917393 | 0.9570312500 | |
| 16 | 1 | 50 | 0.9445463383 | 0.9566326531 | |
| ∗ 16 | 2 | 3 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 4 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 5 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 6 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 7 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 8 | 1.9999999999 | 2.0000000000 | tight bound |
| ∗ 16 | 2 | 9 | 1.9687499999 | 1.9687500000 | |
| ∗ 16 | 2 | 10 | 1.9444444444 | 1.9444444445 | |
| ∗ 16 | 2 | 11 | 1.9249999999 | 1.9250000000 | |
| ∗ 16 | 2 | 12 | 1.9090909090 | 1.9090909091 | |
| ∗ 16 | 2 | 13 | 1.8958333333 | 1.8958333334 | |
| ∗ 16 | 2 | 14 | 1.8846153846 | 1.8846153847 | |
| ∗ 16 | 2 | 15 | 1.8749999999 | 1.8750000000 | |
| ∗ 16 | 2 | 16 | 1.8666666666 | 1.8666666667 | |
| ∗ 16 | 2 | 17 | 1.8593749999 | 1.8593750000 | |
| ∗ 16 | 2 | 18 | 1.8529411764 | 1.8529411765 | |
| ∗ 16 | 2 | 19 | 1.8472222222 | 1.8472222223 | |
| ∗ 16 | 2 | 20 | 1.8421052631 | 1.8421052632 | |
| ∗ 16 | 2 | 21 | 1.8374999999 | 1.8375000000 | |
| ∗ 16 | 2 | 22 | 1.8333333333 | 1.8333333334 | |
| ∗ 16 | 2 | 23 | 1.8295454545 | 1.8295454546 | |
| ∗ 16 | 2 | 24 | 1.8260869565 | 1.8260869566 | |
| ∗ 16 | 2 | 25 | 1.8229166666 | 1.8229166667 | |
| ∗ 16 | 2 | 26 | 1.8199999999 | 1.8200000000 | |
| ∗ 16 | 2 | 27 | 1.8173076923 | 1.8173076924 | |
| ∗ 16 | 2 | 28 | 1.8148148148 | 1.8148148149 | |
| ∗ 16 | 2 | 29 | 1.8124999999 | 1.8125000000 | |
| ∗ 16 | 2 | 30 | 1.8103448275 | 1.8103448276 | |
| ∗ 16 | 2 | 31 | 1.8083333333 | 1.8083333334 | |
| ∗ 16 | 2 | 32 | 1.8064516129 | 1.8064516130 | |
| ∗ 16 | 2 | 33 | 1.8046874999 | 1.8046875000 | |
| ∗ 16 | 2 | 34 | 1.8030303030 | 1.8030303031 | |
| ∗ 16 | 2 | 35 | 1.8014705882 | 1.8014705883 | |
| ∗ 16 | 2 | 36 | 1.7999999999 | 1.8000000000 | |
| ∗ 16 | 2 | 37 | 1.7986111111 | 1.7986111112 | |
| ∗ 16 | 2 | 38 | 1.7972972972 | 1.7972972973 | |
| ∗ 16 | 2 | 39 | 1.7960526315 | 1.7960526316 | |
| ∗ 16 | 2 | 40 | 1.7948717948 | 1.7948717949 | |
| ∗ 16 | 2 | 41 | 1.7937499999 | 1.7937500000 | |
| ∗ 16 | 2 | 42 | 1.7926829268 | 1.7926829269 | |
| ∗ 16 | 2 | 43 | 1.7916666666 | 1.7916666667 | |
| ∗ 16 | 2 | 44 | 1.7906976744 | 1.7906976745 | |
| ∗ 16 | 2 | 45 | 1.7897727272 | 1.7897727273 | |
| ∗ 16 | 2 | 46 | 1.7888888888 | 1.7888888889 | |
| ∗ 16 | 2 | 47 | 1.7880434782 | 1.7880434783 | |
| ∗ 16 | 2 | 48 | 1.7872340425 | 1.7872340426 | |
| 16 | 2 | 49 | 1.7864578165 | 1.7864583334 | |
| 16 | 2 | 50 | 1.7857113491 | 1.7857142858 | |
| 16 | 2 | 64 | 1.7724763231 | 1.7777777778 | |
| ∗ 16 | 3 | 3 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 16 | 3 | 4 | 2.9999999999 | 3.0000000000 | tight bound |
| ∗ 16 | 3 | 5 | 2.9999999999 | 3.0000000000 | tight bound |
| 16 | 3 | 6 | 2.9199999999 | 2.9250000000 | |
| 16 | 3 | 7 | 2.8437499980 | 2.8437500000 | unclear whether bound is tight |
| ∗ 16 | 3 | 8 | 2.7857142857 | 2.7857142858 | |
| ∗ 16 | 3 | 9 | 2.7421874999 | 2.7421875000 | |
| ∗ 16 | 3 | 10 | 2.7083333333 | 2.7083333334 | |
| ∗ 16 | 3 | 11 | 2.6812499999 | 2.6812500000 | |
| ∗ 16 | 3 | 12 | 2.6590909090 | 2.6590909091 | |
| ∗ 16 | 3 | 13 | 2.6406249999 | 2.6406250000 | |
| ∗ 16 | 3 | 14 | 2.6249999999 | 2.6250000000 | |
| ∗ 16 | 3 | 15 | 2.6116071428 | 2.6116071429 | |
| ∗ 16 | 3 | 16 | 2.5999999999 | 2.6000000000 | |
| ∗ 16 | 3 | 17 | 2.5898437499 | 2.5898437500 | |
| ∗ 16 | 3 | 18 | 2.5808823529 | 2.5808823530 | |
| ∗ 16 | 3 | 19 | 2.5729166666 | 2.5729166667 | |
| ∗ 16 | 3 | 20 | 2.5657894736 | 2.5657894737 | |
| ∗ 16 | 3 | 21 | 2.5593749999 | 2.5593750000 | |
| ∗ 16 | 3 | 22 | 2.5535714285 | 2.5535714286 | |
| ∗ 16 | 3 | 23 | 2.5482954545 | 2.5482954546 | |
| ∗ 16 | 3 | 24 | 2.5434782608 | 2.5434782609 | |
| ∗ 16 | 3 | 25 | 2.5390624999 | 2.5390625000 | |
| ∗ 16 | 3 | 26 | 2.5349999999 | 2.5350000000 | |
| ∗ 16 | 3 | 27 | 2.5312499999 | 2.5312500000 | |
| ∗ 16 | 3 | 28 | 2.5277777777 | 2.5277777778 | |
| ∗ 16 | 3 | 29 | 2.5245535714 | 2.5245535715 | |
| ∗ 16 | 3 | 30 | 2.5215517241 | 2.5215517242 | |
| ∗ 16 | 3 | 31 | 2.5187499999 | 2.5187500000 | |
| ∗ 16 | 3 | 32 | 2.5161290322 | 2.5161290323 | |
| ∗ 16 | 3 | 33 | 2.5136718749 | 2.5136718750 | |
| ∗ 16 | 3 | 34 | 2.5113636363 | 2.5113636364 | |
| ∗ 16 | 3 | 35 | 2.5091911764 | 2.5091911765 | |
| ∗ 16 | 3 | 36 | 2.5071428571 | 2.5071428572 | |
| ∗ 16 | 3 | 37 | 2.5052083333 | 2.5052083334 | |
| ∗ 16 | 3 | 38 | 2.5033783783 | 2.5033783784 | |
| ∗ 16 | 3 | 39 | 2.5016447368 | 2.5016447369 | |
| ∗ 16 | 3 | 40 | 2.4999999999 | 2.5000000000 | |
| ∗ 16 | 3 | 41 | 2.4984374999 | 2.4984375000 | |
| ∗ 16 | 3 | 42 | 2.4969512195 | 2.4969512196 | |
| ∗ 16 | 3 | 43 | 2.4955357142 | 2.4955357143 | |
| ∗ 16 | 3 | 44 | 2.4941860465 | 2.4941860466 | |
| ∗ 16 | 3 | 45 | 2.4928977272 | 2.4928977273 | |
| ∗ 16 | 3 | 46 | 2.4916666666 | 2.4916666667 | |
| ∗ 16 | 3 | 47 | 2.4904891304 | 2.4904891305 | |
| ∗ 16 | 3 | 48 | 2.4893617021 | 2.4893617022 | |
| ∗ 16 | 3 | 49 | 2.4882812499 | 2.4882812500 | |
| ∗ 16 | 3 | 50 | 2.4872448979 | 2.4872448980 | |
| ∗ 16 | 3 | 64 | 2.4761904761 | 2.4761904762 | |
| 16 | 3 | 80 | 2.4667347824 | 2.4683544304 |
References
- A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor, and N. J. A. Sloane, A group-theoretic framework for the construction of packings in Grassmannian spaces, J. Algebraic Combin. 9 (1999), 129–140, doi:10.1023/A:1018673825179, arXiv:math/0208002.
- H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
- H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
- H. Cohn, A. Kumar, and G. Minton, Optimal simplices and codes in projective spaces, Geom. Topol. 20 (2016), 1289–1357, doi:10.2140/gt.2016.20.1289, arXiv:1308.3188.
- J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645.