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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.
6,662,718 matroids, showing 20,651–20,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70332 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70333 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70335 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70336 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70337 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70339 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70340 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70341 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70343 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70344 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70345 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70353 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70354 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70355 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70357 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.70358 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70359 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70361 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.70362 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70363 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70372 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70373 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70374 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70375 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70377 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70378 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70379 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70380 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70382 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70383 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70384 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70385 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70387 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70388 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70389 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70390 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70391 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70395 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70399 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70404 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70405 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70406 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70407 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70408 | 3 | 11 | 150 | 2 | ✓ | all | 3 | rational |
| 3.11.70412 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70413 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70414 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70415 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70418 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70419 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |