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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 19,501–19,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.74276 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74282 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74296 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74301 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74302 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74303 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74304 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74305 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74309 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74313 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74320 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74325 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.74332 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74341 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74342 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74343 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74344 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74345 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74346 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74351 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74355 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74359 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74362 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74378 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74381 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74388 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74409 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74415 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74465 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74466 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74467 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74468 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74469 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74470 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74472 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74473 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74474 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74475 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74476 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74478 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74479 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74480 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74481 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74482 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74484 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74485 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74486 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74487 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74488 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74489 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |