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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 20,501–20,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.69947 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69948 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69949 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69951 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.69952 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69953 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69956 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69957 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69958 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69959 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69961 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69962 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69963 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69965 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69972 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69973 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69978 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69979 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69988 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69989 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational |
| 3.11.69990 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.69992 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69993 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69995 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.69998 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.69999 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70000 | 3 | 11 | 151 | 1 | ✓ | all | 3 | genus 1 curve (11a3) x P^1 |
| 3.11.70003 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70011 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70012 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70014 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.70015 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70017 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70019 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70020 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70021 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70024 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70032 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70033 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70034 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70036 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70038 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70040 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70041 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70042 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70045 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70046 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70095 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70096 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70097 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |