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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.
6,662,718 matroids, showing 20,451–20,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.69800 | 3 | 11 | 152 | 1 | ✓ | all | 3 | empty |
| 3.11.69802 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69803 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69804 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.69805 | 3 | 11 | 152 | 1 | ✓ | all | 3 | empty |
| 3.11.69806 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.69811 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69815 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69826 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69827 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69829 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69830 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69832 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69833 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69836 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69837 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69838 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69839 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69841 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69850 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69851 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69852 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69853 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69855 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69857 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69860 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69861 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69862 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69863 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69864 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69866 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69911 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69912 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69913 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69914 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69916 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69917 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69918 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69919 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69921 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69922 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69923 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69926 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69927 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69928 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69929 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69934 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69936 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69938 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69946 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |