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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 20,751–20,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.70516 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70517 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70518 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70522 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70524 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70527 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70528 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70529 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70530 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70533 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70535 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70536 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70537 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70538 | 3 | 11 | 150 | 1 | ✓ | all | 3 | empty |
| 3.11.70541 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70543 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70545 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70546 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70547 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70548 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70551 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70561 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70562 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70563 | 3 | 11 | 150 | 2 | ✓ | all | 3 | rational |
| 3.11.70564 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70566 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70567 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70569 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70570 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70572 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70574 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70575 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.70576 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70577 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70578 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70582 | 3 | 11 | 150 | 2 | ✓ | all | 3 | empty |
| 3.11.70584 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70587 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70588 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.70589 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.70590 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.70593 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70596 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70597 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70598 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.70599 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70602 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.70603 | 3 | 11 | 152 | 2 | ✓ | all | 3 | rational |
| 3.11.70605 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.70606 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |