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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.
1,370,992 matroids, showing 18,801–18,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.257618 | 3 | 11 | 144 | 24 | ✓ | all | 5 | rational |
| 3.11.257623 | 3 | 11 | 146 | 12 | ✓ | all | 5 | rational |
| 3.11.257625 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257626 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257628 | 3 | 11 | 145 | 24 | ✓ | all | 5 | rational |
| 3.11.257629 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257630 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257632 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257633 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257634 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257638 | 3 | 11 | 145 | 12 | ✓ | all | 5 | rational |
| 3.11.257640 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257642 | 3 | 11 | 144 | 72 | ✓ | all | 5 | rational |
| 3.11.257644 | 3 | 11 | 148 | 8 | ✓ | all | 5 | rational |
| 3.11.257645 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.257646 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257647 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.257656 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257657 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257658 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.257659 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257660 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.257662 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257663 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.257664 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257665 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257666 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257669 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257671 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.257672 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257673 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257674 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.257675 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257676 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257677 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257683 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257689 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257693 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257695 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.257696 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257697 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257698 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257699 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257702 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257705 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257711 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257712 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257714 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257718 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.257732 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |