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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 19,451–19,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.74152 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74153 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74154 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74156 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74157 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74158 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74159 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74160 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74161 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74162 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74167 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74171 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74176 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74177 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74178 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74179 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74180 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74181 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74186 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74191 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74192 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74193 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.74194 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74195 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74200 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74201 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74202 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74203 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74204 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74205 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74206 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74211 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74216 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.74220 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74225 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74226 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74227 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74228 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74231 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74235 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74236 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74237 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74238 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74239 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74240 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.74246 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74247 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74252 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74256 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74267 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |