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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 20,951–21,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70961 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70963 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70964 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70965 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70966 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70967 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70968 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70972 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70974 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70977 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70978 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.70979 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70980 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |
| 3.11.70988 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70989 | 3 | 11 | 150 | 2 | ✓ | all | 3 | empty |
| 3.11.70990 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70991 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70992 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70994 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70995 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70996 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70997 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70999 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71000 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71001 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71002 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71004 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71005 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71006 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.71007 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71011 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71014 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71018 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.71019 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71020 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71021 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71022 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.71024 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71027 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71028 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71029 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71030 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71032 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71034 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71037 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71038 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71039 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71040 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71042 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71045 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |