All matroids
Every matroid ever to enter the record book. A current holder has the best verified α over one of GF(2), GF(3), GF(4), GF(5), GF(7), or reached 4/3; every other row is kept as history. Click a column header to sort; click again to reverse.
showing 19 of 19 matroids
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| matroid | n | rank | bases | α | ≈ | description | status | discovered by | submitter | submitted |
|---|---|---|---|---|---|---|---|---|---|---|
| #1 | 10 | 5 | 136 | 8/7 | 1.1429 | matrix GF(2) | GF(2) record | June Huh, Benjamin Schröter, Botong Wang | David Renshaw | 2026-08-05 15:25:29 |
| #2 | 14 | 5 | 891 | 8/7 | 1.1429 | matrix GF(3) | history | June Huh, Benjamin Schröter, Botong Wang | David Renshaw | 2026-08-05 15:25:29 |
| #5 | 18 | 5 | 3,392 | 8/7 | 1.1429 | matrix GF(4) | history | Construction: Huh–Schröter–Wang; instantiated over GF(4) for this site | David Renshaw | 2026-08-05 17:09:19 |
| #4 | 22 | 5 | 9,625 | 8/7 | 1.1429 | matrix GF(5) | history | June Huh, Benjamin Schröter, Botong Wang | David Renshaw | 2026-08-05 15:39:09 |
| #7 | 30 | 5 | 46,991 | 8/7 | 1.1429 | matrix GF(7) | history | June Huh, Benjamin Schröter, Botong Wang | David Renshaw | 2026-08-05 17:26:47 |
| #6 | 26 | 9 | 1,518,400 | 280043/243256 | 1.1512 | matrix GF(7) | history | Chris Eur | David Renshaw | 2026-08-05 17:26:29 |
| #13 | 26 | 9 | 1,131,928 | 55752/48391 | 1.1521 | matrix GF(4) | history | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 08:11:58 |
| #10 | 26 | 9 | 1,520,989 | 561630/487297 | 1.1525 | matrix GF(7) | history | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 05:45:32 |
| #9 | 22 | 9 | 176,265 | 4664/4007 | 1.1640 | matrix GF(5) | history | Chris Eur | Christopher Eur | 2026-08-06 20:33:30 |
| #11 | 26 | 9 | 1,547,573 | 98252/84369 | 1.1646 | matrix GF(7) | history | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 06:55:20 |
| #14 | 25 | 13 | 661,932 | 2915/2484 | 1.1735 | matrix GF(4) | history | Jeewon Kim | Jeewon Kim | 2026-08-09 14:01:01 |
| #19 | 17 | 10 | 1,816 | 27/23 | 1.1739 | matrix GF(4) | history | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 18:40:08 |
| #12 | 26 | 9 | 1,478,356 | 147888/125779 | 1.1758 | matrix GF(7) | history | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 08:00:25 |
| #20 | 24 | 13 | 160,704 | 875/744 | 1.1761 | matrix GF(4) | GF(4) record | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 18:56:27 |
| #15 | 23 | 13 | 234,056 | 15750/13283 | 1.1857 | matrix GF(5) | history | Jeewon Kim | Jeewon Kim | 2026-08-09 14:04:27 |
| #18 | 25 | 13 | 560,422 | 1045392/880397 | 1.1874 | matrix GF(5) | GF(5) record | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 18:34:38 |
| #16 | 23 | 13 | 77,827 | 40500/33827 | 1.1973 | matrix GF(7) | history | Jeewon Kim | Jeewon Kim | 2026-08-09 14:07:17 |
| #17 | 23 | 13 | 439,775 | 63/52 | 1.2115 | matrix GF(7) | GF(7) record | Yongxi (Aaron) Lin | Yongxi (Aaron) Lin | 2026-08-09 17:25:10 |
| #3 | 12 | 6 | 684 | 100/81 | 1.2346 | matrix GF(3) | GF(3) record | Chris Eur and David Renshaw; independently June Huh | David Renshaw | 2026-08-05 15:25:29 |