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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 19,701–19,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7757 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7758 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7759 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7760 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7761 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7762 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7763 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7764 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7765 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7766 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7767 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7768 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7769 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7770 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7771 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7772 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7773 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7774 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7775 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7776 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7777 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7778 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7779 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7780 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7781 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7782 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7783 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7784 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7785 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7786 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7787 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7788 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7789 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7790 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7791 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7792 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7793 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7794 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7795 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7796 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7797 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7798 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7799 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7800 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7801 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7802 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7803 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7804 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7805 | 3 | 11 | 153 | 1 | ✓ | all | 2 | K3 surface |
| 3.11.7806 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |