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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.
1,370,992 matroids, showing 18,951–19,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.258097 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258098 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258099 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258100 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258101 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258107 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.258113 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258119 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258121 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258122 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.258123 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258124 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258125 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258126 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258127 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258132 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.258136 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258140 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258142 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.258143 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.258144 | 3 | 11 | 148 | 1 | ✓ | all | 5 | rational |
| 3.11.258145 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258146 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258147 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258148 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258154 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258159 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258164 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258169 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258174 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258175 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258196 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258218 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258241 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258257 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258258 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.258259 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258260 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258261 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258262 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258263 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258269 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258275 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258280 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258285 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258290 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258311 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258312 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258344 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258377 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |