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…or describe it by its bases, non-bases or lines
Matroid

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.

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Invariants
Realizability
Properties

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5,849,183 matroids, showing 22,151–22,200

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.1844353111491✓all1rational
3.11.1844383111481✓all1rational
3.11.1844403111501✓all1rational
3.11.1844433111491✓all1rational
3.11.1844473111481✓all1rational
3.11.1844503111481✓all1rational
3.11.1844533111481✓all1rational
3.11.1844553111481✓all but 21rational
3.11.1844563111481✓all1rational
3.11.1844573111481✓all1rational
3.11.1844583111471✓all1point over Q(a)/(a^3 - a^2 - 2*a + 1)
3.11.1844613111471✓all1point over Q(a)/(a^2 - a - 1)
3.11.1844663111481✓all but 21rational
3.11.1844693111481✓all1rational
3.11.1844713111491✓all1rational
3.11.1844733111481✓all1empty
3.11.1844743111491✓all1rational
3.11.1844753111481✓all but 21rational
3.11.1844783111471✓all1empty
3.11.1844843111471✓all1empty
3.11.1844853111501✓all but 21rational
3.11.1844863111491✓all1rational
3.11.1844883111491✓all1rational
3.11.1844893111481✓all1rational
3.11.1844913111491✓all1rational
3.11.1844923111481✓all1rational
3.11.1844983111481✓all1empty
3.11.1844993111524✓all1rational
3.11.1845003111514✓all1rational
3.11.1845063111511✓all but 21rational
3.11.1845083111502✓all1rational
3.11.1845093111502✓all1rational
3.11.1845183111512✓all but 21rational
3.11.1845213111501✓all but 21rational
3.11.1845233111491✓all1rational
3.11.1845243111501✓all but 2,31rational
3.11.1845263111512✓all but 21rational
3.11.1845273111502✓all but 21empty
3.11.1845553111502✓all1rational
3.11.1845573111492✓all1rational
3.11.1845583111501✓all but 21rational
3.11.1845613111502✓all1rational
3.11.1845623111492✓all but 21rational
3.11.1845683111492✓all1rational
3.11.1845693111492✓all1rational
3.11.1845713111491✓all1rational
3.11.1845723111481✓all1rational
3.11.1845743111481✓all but 21rational
3.11.1845753111491✓all but 2,3,51rational
3.11.1845763111482✓all but 2,51rational

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