| r | n (this family) | p(H) bound | density | published n | published form | improvement |
|---|---|---|---|---|---|---|
| 10 | 50 | 10 | 1.24609 | 51 | KR 2003 | -1 |
| 12 | — | — | — | 107 | phi(12) | not reachable by QM_2^2 |
| 14 | — | — | — | 215 | phi(14) | not reachable by QM_2^2 |
| 16 | — | — | — | 431 | phi(16) | not reachable by QM_2^2 |
| 18 | 815 | 33 | 1.26847 | 831 | Phi(18) | -16 |
| 20 | 1631 | 65 | 1.26924 | 1663 | Phi(20) | -32 |
| 22 | — | — | — | 3389 | Phihat(22) | not reachable by QM_2^2 |
| 24 | — | — | — | 6781 | Phihat(24) | not reachable by QM_2^2 |
| 26 | — | — | — | 13565 | Phihat(26) | not reachable by QM_2^2 |
| 28 | — | — | — | 26623 | Phi(28) | not reachable by QM_2^2 |
| 30 | 52223 | 129 | 1.27000 | 53247 | Phi(30) | -1024 |
| 32 | 104447 | 257 | 1.27001 | 106495 | Phi(32) | -2048 |
| 34 | 208895 | 257 | 1.27001 | 212991 | Phi(34) | -4096 |
| 36 | 417791 | 513 | 1.27002 | 425983 | Phi(36) | -8192 |
| 38 | 835583 | 1025 | 1.27002 | 851967 | Phi(38) | -16384 |
| 40 | 1671167 | 2049 | 1.27002 | 1703935 | Phi(40) | -32768 |
| 42 | — | — | — | 3407871 | Phi(42) | not reachable by QM_2^2 |
| 44 | — | — | — | 6815743 | Phi(44) | not reachable by QM_2^2 |
| 46 | 13369343 | 513 | 1.27002 | 13631487 | Phi(46) | -262144 |
| 48 | 26738687 | 1025 | 1.27002 | 27262975 | Phi(48) | -524288 |
| 50 | 53477375 | 1025 | 1.27002 | 54525951 | Phi(50) | -1048576 |
| 52 | 106954751 | 1025 | 1.27002 | 109051903 | Phi(52) | -2097152 |
| 54 | 213909503 | 2049 | 1.27002 | 218103807 | Phi(54) | -4194304 |
| 56 | 427819007 | 2049 | 1.27002 | 436207615 | Phi(56) | -8388608 |
| 58 | 855638015 | 4097 | 1.27002 | 872415231 | Phi(58) | -16777216 |
| 60 | 1711276031 | 4097 | 1.27002 | 1744830463 | Phi(60) | -33554432 |
| 62 | 3422552063 | 8193 | 1.27002 | 3489660927 | Phi(62) | -67108864 |
| 64 | 6845104127 | 8193 | 1.27002 | 6979321855 | Phi(64) | -134217728 |
files / problems / covering / share / 2026-08-16 / result / data / family_table.md