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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 20,901–20,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70870 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70871 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70872 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70874 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70875 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70876 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70885 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70886 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70887 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70888 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70890 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70891 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70893 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70894 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70902 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70903 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70904 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70906 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70907 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70909 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70910 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70911 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70913 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70914 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70915 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70923 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70924 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70925 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70927 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70928 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70929 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70931 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70932 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70933 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70942 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70943 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70944 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70945 | 3 | 11 | 151 | 2 | ✓ | all | 3 | empty |
| 3.11.70947 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70948 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70949 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70950 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70951 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70953 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70954 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70955 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70956 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70958 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70959 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70960 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |