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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 20,401–20,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.69664 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69665 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69666 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69668 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69669 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.69671 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69672 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69674 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69683 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69684 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69685 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69688 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69689 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69691 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69692 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69702 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69703 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69704 | 3 | 11 | 155 | 1 | ✓ | all | 3 | rational |
| 3.11.69705 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69707 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69709 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69758 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69759 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69760 | 3 | 11 | 152 | 1 | ✓ | all | 3 | empty |
| 3.11.69761 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69763 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69764 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69765 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69766 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69767 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69769 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69770 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69771 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69772 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69774 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69775 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69776 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69777 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69786 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69787 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69788 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69789 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69790 | 3 | 11 | 152 | 1 | ✓ | all | 3 | empty |
| 3.11.69792 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69793 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69794 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69795 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69797 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69798 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69799 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |