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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 20,601–20,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70198 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70199 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70200 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70201 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70202 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70204 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70207 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70209 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70210 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70212 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70220 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70221 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70223 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70224 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70226 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70227 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70230 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70231 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70232 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70233 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70234 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.70236 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70239 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70241 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70287 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70288 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70289 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70290 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70292 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70293 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70294 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70295 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70297 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70298 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.70299 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70300 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70302 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70303 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70304 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70305 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70313 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70314 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70315 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70317 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70318 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70319 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70321 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70322 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70323 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70331 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |