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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 19,551–19,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.74491 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.74492 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74493 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74494 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74495 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74496 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74497 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74502 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74506 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74513 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74514 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74515 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74516 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74517 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74518 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74523 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74528 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74529 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74530 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74531 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74532 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74533 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74538 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74539 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74540 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74541 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74542 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74543 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74544 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74549 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74554 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74560 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74566 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74567 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74568 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74569 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74572 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74575 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74579 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74580 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74581 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.74582 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74585 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74588 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74592 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74593 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74594 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74595 | 3 | 11 | 151 | 1 | ✓ | all | 4 | K3 surface |
| 3.11.74596 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74597 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |