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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.
1,370,992 matroids, showing 18,851–18,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.257733 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257734 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257735 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257736 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257737 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257738 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257740 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257741 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257742 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257743 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257744 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257745 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257746 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257752 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257754 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257755 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257756 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257757 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257758 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257759 | 3 | 11 | 144 | 6 | ✓ | all | 5 | rational |
| 3.11.257760 | 3 | 11 | 148 | 4 | ✓ | all | 5 | rational |
| 3.11.257766 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257772 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257774 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257775 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257776 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257777 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257778 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257779 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257780 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257786 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257792 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257797 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257799 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257800 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257801 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257802 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257803 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257804 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257805 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257810 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257814 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257819 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.257820 | 3 | 11 | 145 | 4 | ✓ | all | 5 | rational |
| 3.11.257821 | 3 | 11 | 145 | 12 | ✓ | all | 5 | empty |
| 3.11.257822 | 3 | 11 | 148 | 8 | ✓ | all | 5 | rational |
| 3.11.257823 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257824 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.257825 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257831 | 3 | 11 | 146 | 8 | ✓ | all | 5 | rational |