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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 21,001–21,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71046 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71047 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71048 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71049 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71054 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71058 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71062 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71068 | 3 | 11 | 150 | 2 | ✓ | all | 3 | rational |
| 3.11.71079 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71080 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71081 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71082 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71084 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71085 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71087 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71088 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71090 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71092 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71093 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71094 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71095 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71098 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71100 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71103 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71105 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71106 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71108 | 3 | 11 | 151 | 1 | ✓ | all | 3 | K3 surface |
| 3.11.71111 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71112 | 3 | 11 | 151 | 1 | ✓ | all | 3 | K3 surface |
| 3.11.71113 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71114 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71117 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71119 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71121 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71122 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71123 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71124 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71126 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71129 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71130 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71131 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71132 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71133 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71137 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.71140 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.71143 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71149 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71162 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71163 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71164 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |