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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 20,851–20,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70715 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70716 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70718 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70720 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70728 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70729 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70731 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70732 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70733 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70734 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70737 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70738 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70739 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70740 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70749 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70751 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70757 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70759 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70760 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70761 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70763 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70764 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70765 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70767 | 3 | 11 | 152 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70768 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70769 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70771 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70775 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70780 | 3 | 11 | 152 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70781 | 3 | 11 | 152 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70784 | 3 | 11 | 152 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70787 | 3 | 11 | 152 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70796 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70797 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70799 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70801 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70804 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70805 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70806 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70807 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70810 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70811 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70812 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.70861 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70862 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70863 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70865 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70866 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70867 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70868 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |