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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 19,701–19,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75000 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75001 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75010 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75011 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75012 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75013 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75014 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75015 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75016 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75021 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75022 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75032 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75041 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75045 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75049 | 3 | 11 | 150 | 1 | ✓ | all | 4 | empty |
| 3.11.75067 | 3 | 11 | 150 | 1 | ✓ | all | 4 | genus 1 curve (17a4) |
| 3.11.75089 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.75105 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75124 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75125 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75126 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.75127 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.75128 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75129 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75134 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.75138 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.75139 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75142 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75157 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75166 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75172 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75194 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75216 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75232 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75251 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75252 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.75254 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75256 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75261 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75266 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75273 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75285 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75300 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75302 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75304 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75305 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75306 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75307 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75310 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75311 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |