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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 20,701–20,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70423 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70424 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70425 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70426 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70429 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70437 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70438 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70439 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70440 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70442 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70443 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70445 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70446 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70448 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70449 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70451 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70452 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70453 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70454 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70455 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70459 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70461 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70464 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70465 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70466 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70467 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70468 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70472 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70474 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70476 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70477 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70478 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70479 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70482 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70484 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70486 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70487 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70488 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70489 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70492 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70502 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70503 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70504 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70505 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70507 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70508 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70510 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70511 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70514 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70515 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |