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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.
32,400,859 matroids, showing 19,951–20,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.8007 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8008 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8009 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8010 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8011 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8012 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8013 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8014 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8015 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8016 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8017 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8018 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8019 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8020 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8021 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.8022 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8023 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8024 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8025 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8026 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8027 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.8028 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.8029 | 3 | 11 | 154 | 2 | ✓ | all | 3 | K3 surface x P^1 |
| 3.11.8030 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8031 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8032 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8033 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8034 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8035 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8036 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8037 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8038 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8039 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8040 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.8041 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.8042 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8043 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8044 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8045 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8046 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8047 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.8048 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.8049 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8050 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8051 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8052 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8053 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8054 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.8055 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.8056 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |