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…or describe it by its bases, non-bases or lines
Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id.
Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as
123 145. Lines are the lines with at least three points of a simple rank-3 matroid.
A revlex encoding is a string of * and 0.
3,622,905 matroids, showing 19,651–19,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.74895 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74896 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74897 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74902 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74903 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74904 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74905 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74906 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74907 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74908 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74913 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74919 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74920 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74921 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74922 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.74923 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.74924 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.74929 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74930 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74932 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74933 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74934 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74935 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.74936 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74937 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74938 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74943 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74944 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74950 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74951 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.74952 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74953 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74954 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74955 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74956 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74961 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74962 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74973 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74974 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74975 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74976 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.74977 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.74978 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74982 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74991 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74992 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74993 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74994 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74995 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74996 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |