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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 20,551–20,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70098 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70100 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70101 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70102 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70103 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70105 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70106 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70107 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70108 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70110 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70111 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70112 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70113 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70114 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70119 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70121 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70123 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70138 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70139 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70140 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70141 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70143 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70144 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70145 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70146 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70148 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70149 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70150 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70151 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70152 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70155 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70156 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70157 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70158 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70159 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70163 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70167 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70173 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70174 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70176 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70177 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70185 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70186 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70187 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70188 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70190 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70191 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70193 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70194 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70196 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |