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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.
5,849,183 matroids, showing 21,751–21,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.181571 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181572 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181574 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.181575 | 3 | 11 | 151 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181577 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181578 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181580 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181581 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181686 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181754 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181756 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181757 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181797 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182216 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182217 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.182219 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182220 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182246 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182247 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182249 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182250 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182255 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182257 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182282 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182283 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182285 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182286 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182292 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182293 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.182295 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182296 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182302 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182304 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182440 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182441 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182443 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182444 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182485 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182486 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182488 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182489 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182494 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182496 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182521 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182522 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182524 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182525 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.182531 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.182537 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.182538 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |