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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 19,151–19,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.73344 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73345 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73346 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73350 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73353 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73356 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73360 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73361 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.73362 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.73363 | 3 | 11 | 156 | 2 | ✓ | all | 4 | rational |
| 3.11.73364 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.73365 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.73369 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.73372 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.73376 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73377 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73378 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73379 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73380 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73381 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73382 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.73387 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73390 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73393 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73396 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73408 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.73422 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73435 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73436 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73437 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73438 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73439 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73440 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73444 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73447 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73450 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73463 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73464 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73465 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73466 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73467 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73468 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73469 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73474 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73477 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73480 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.73495 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73496 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.73497 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73498 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |