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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.
5,849,183 matroids, showing 22,401–22,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.185940 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185948 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185949 | 3 | 11 | 147 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.185951 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185953 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185955 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185957 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185958 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185966 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185967 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185968 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185970 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^4 - a^3 + 2*a - 1) |
| 3.11.185971 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.185972 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185975 | 3 | 11 | 152 | 1 | ✓ | all | 1 | rational |
| 3.11.185976 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.185977 | 3 | 11 | 151 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.185978 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.185981 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.185993 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185999 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186034 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186035 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186036 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186038 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186039 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186040 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186042 | 3 | 11 | 150 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.186043 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186044 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186045 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186055 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186056 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186058 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186059 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186061 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186062 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186063 | 3 | 11 | 150 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.186065 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186071 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186072 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186073 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186076 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186077 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186079 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186080 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186081 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186083 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186084 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186085 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |