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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 19,351–19,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.73856 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73857 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73859 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73860 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73864 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73870 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73880 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73881 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73882 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73883 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73884 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73885 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73887 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73888 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73889 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73890 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.73891 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73893 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73894 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.73895 | 3 | 11 | 151 | 2 | ✓ | all | 4 | K3 surface |
| 3.11.73896 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73898 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73899 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73900 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73901 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73903 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73904 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73905 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73906 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73907 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73908 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73909 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73914 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73917 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.73922 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73923 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73924 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73925 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73926 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73927 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73932 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73937 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.73938 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73939 | 3 | 11 | 151 | 1 | ✓ | all | 4 | empty |
| 3.11.73940 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73941 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73945 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.73946 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73947 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.73948 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |