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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 18,901–18,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.257836 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257841 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257846 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257851 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257852 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257872 | 3 | 11 | 144 | 12 | ✓ | all | 5 | rational |
| 3.11.257894 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257917 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257933 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257934 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257936 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257938 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257942 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257946 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.257951 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257964 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257980 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258013 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258020 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258021 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258023 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258026 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258030 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258037 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258054 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258055 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258056 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258057 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258058 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258059 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258060 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258062 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258063 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258064 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258065 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258066 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258067 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258068 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258074 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258076 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258077 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258078 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258079 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258080 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258081 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258082 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258088 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258093 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.258095 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258096 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |