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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.
32,400,859 matroids, showing 19,101–19,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7157 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7158 | 3 | 11 | 153 | 6 | ✓ | all but 2 | 2 | rational |
| 3.11.7159 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7160 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7161 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7162 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7163 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7164 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7165 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7166 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7167 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7168 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7169 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7170 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7171 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7172 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7173 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7174 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7175 | 3 | 11 | 155 | 4 | ✓ | all | 4 | rational |
| 3.11.7176 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7177 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7178 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7179 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7180 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7181 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7182 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.7183 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7184 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7185 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7186 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7187 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7188 | 3 | 11 | 158 | 1 | ✓ | all | 7 | rational |
| 3.11.7189 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7190 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7191 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7192 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7193 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7194 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7195 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7196 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7197 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7198 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7199 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7200 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7201 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7202 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7203 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7204 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7205 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7206 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |