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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 21,251–21,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71697 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71698 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71699 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71701 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71702 | 3 | 11 | 150 | 2 | ✓ | all | 3 | rational |
| 3.11.71703 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71704 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71706 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71707 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71708 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71709 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71712 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71716 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71720 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71721 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71722 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71723 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71726 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71730 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71731 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71732 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71733 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71736 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71738 | 3 | 11 | 151 | 2 | ✓ | all | 3 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.71742 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71743 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71744 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71745 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71748 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71752 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71753 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71754 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71755 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71756 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71760 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71765 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71769 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71777 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71778 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71780 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71782 | 3 | 11 | 151 | 1 | ✓ | all | 3 | genus 1 curve (14a4) x P^1 |
| 3.11.71792 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71793 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71794 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71795 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71797 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71798 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71800 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71801 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71803 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |