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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 19,751–19,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75312 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75314 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75315 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75316 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75318 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75319 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75320 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75321 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75323 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.75325 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75327 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75330 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75334 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75335 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75336 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75337 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75339 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75342 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75345 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75349 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75353 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75354 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75355 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75356 | 3 | 11 | 150 | 1 | ✓ | all | 4 | empty |
| 3.11.75357 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75358 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75361 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75365 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75374 | 3 | 11 | 150 | 1 | ✓ | all | 4 | genus 1 curve (14a4) |
| 3.11.75375 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75376 | 3 | 11 | 154 | 4 | ✓ | all | 4 | rational |
| 3.11.75377 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.75378 | 3 | 11 | 152 | 4 | ✓ | all | 4 | rational |
| 3.11.75379 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.75383 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75386 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.75395 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75396 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75397 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75398 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75399 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75400 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75405 | 3 | 11 | 156 | 2 | ✓ | all | 4 | rational |
| 3.11.75409 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.75411 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.75414 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.75418 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75433 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75442 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75451 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |