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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.
32,400,859 matroids, showing 19,351–19,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7407 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7408 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7409 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7410 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7411 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7412 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7413 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7414 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7415 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7416 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7417 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7418 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7419 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7420 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7421 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7422 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7423 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7424 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7425 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7426 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7427 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7428 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7429 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7430 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7431 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7432 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7433 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7434 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7435 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7436 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7437 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7438 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7439 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7440 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7441 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7442 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7443 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7444 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7445 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7446 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7447 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7448 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7449 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7450 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7451 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7452 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7453 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7454 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7455 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7456 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |