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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 20,251–20,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.68933 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.68934 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68936 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68937 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68939 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68940 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68945 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68947 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68948 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68950 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68951 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.68952 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68953 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68955 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.68956 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68958 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.68984 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68985 | 3 | 11 | 155 | 2 | ✓ | all | 3 | rational |
| 3.11.68986 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68988 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68989 | 3 | 11 | 155 | 1 | ✓ | all | 3 | rational |
| 3.11.68991 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68992 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.68994 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.68995 | 3 | 11 | 155 | 1 | ✓ | all | 3 | rational |
| 3.11.68996 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.68999 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.69002 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.69004 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69005 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69012 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69013 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69014 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69015 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69017 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69018 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69020 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69024 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69026 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69027 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69029 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69030 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69031 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69032 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69034 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.69035 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69055 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69057 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69059 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.69063 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |