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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.
3,622,905 matroids, showing 19,951–20,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75878 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75879 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75880 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75881 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75882 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75883 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75889 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75890 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75894 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75902 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75910 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75914 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75916 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75917 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75922 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75927 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75942 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75943 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75944 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75945 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75946 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75947 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75949 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75950 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75951 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75952 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75953 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75955 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75956 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.75957 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.75958 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75959 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75961 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75962 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75963 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75964 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75965 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75966 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75967 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75972 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75977 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75978 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75979 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75980 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75981 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75982 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75983 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75988 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75994 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75995 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |