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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 19,401–19,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.73949 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73950 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73951 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73956 | 3 | 11 | 150 | 2 | ✓ | all | 4 | rational |
| 3.11.73960 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73964 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73969 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73970 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73971 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73972 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73973 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73974 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73980 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73981 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73985 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73989 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73999 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74008 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74012 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74025 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74026 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74027 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74028 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74029 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74030 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74035 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74039 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74042 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74045 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74060 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74062 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74069 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74089 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74132 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74133 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74134 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74135 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74136 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74137 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74139 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74140 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74141 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74142 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74143 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74145 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74146 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74147 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74148 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74149 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74151 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |