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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 19,751–19,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7807 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7808 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7809 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7810 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7811 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7812 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7813 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7814 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7815 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7816 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7817 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7818 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7819 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7820 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7821 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7822 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7823 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7824 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7825 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7826 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7827 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7828 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7829 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7830 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7831 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7832 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7833 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7834 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7835 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7836 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7837 | 3 | 11 | 153 | 1 | ✓ | all | 2 | rational |
| 3.11.7838 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7839 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7840 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7841 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7842 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7843 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7844 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7845 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7846 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7847 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7848 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7849 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.7850 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7851 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7852 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7853 | 3 | 11 | 153 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7854 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7855 | 3 | 11 | 153 | 1 | ✓ | all | 2 | K3 surface |
| 3.11.7856 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |