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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 19,251–19,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.73640 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73641 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73642 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73643 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73645 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73647 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73649 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73650 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73651 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73652 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73653 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73654 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73655 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73660 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73663 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73664 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73665 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73666 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73667 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73668 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73669 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73674 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73676 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73678 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.73691 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73693 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73694 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73695 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73696 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73697 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73698 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73703 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73704 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73706 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73708 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73714 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73718 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73720 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73721 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73723 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73724 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73725 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73727 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73738 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73739 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73740 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73741 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73742 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73743 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73745 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |