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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 20,201–20,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.68692 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68700 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.68702 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68710 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68711 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68713 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68720 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68721 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68723 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68724 | 3 | 11 | 152 | 1 | ✓ | all | 3 | K3 surface x P^1 |
| 3.11.68731 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68732 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68734 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68735 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68737 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68739 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68740 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68857 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68859 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68860 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68886 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68887 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68888 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68889 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68891 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68892 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68893 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68895 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68896 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68897 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68899 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.68900 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68901 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68903 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68904 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68905 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68906 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68909 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.68911 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68913 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68914 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68916 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68917 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68925 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.68926 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68927 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68928 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.68929 | 3 | 11 | 155 | 2 | ✓ | all | 3 | rational |
| 3.11.68931 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68932 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |