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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 21,051–21,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71165 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71167 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71169 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71170 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71172 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71174 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71175 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71176 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71177 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71180 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.71181 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.71184 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71185 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71186 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71187 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71189 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71192 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71193 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71194 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71195 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71198 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71199 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71201 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71202 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71203 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71204 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71207 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71208 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71211 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71212 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71213 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71214 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71215 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71219 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71221 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71223 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71228 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71241 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71242 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71243 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71245 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71246 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71247 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71248 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71250 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.71251 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71252 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71254 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71255 | 3 | 11 | 150 | 2 | ✓ | all | 3 | empty |
| 3.11.71256 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |