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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 19,251–19,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7307 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7308 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7309 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7310 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7311 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7312 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7313 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7314 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7315 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7316 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7317 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7318 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7319 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7320 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7321 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7322 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7323 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7324 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7325 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7326 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7327 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7328 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7329 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7330 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7331 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7332 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7333 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7334 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7335 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7336 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7337 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7338 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7339 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7340 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7341 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7342 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7343 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7344 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7345 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7346 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7347 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7348 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7349 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7350 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7351 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7352 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7353 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7354 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7355 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7356 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |