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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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8,076,768 matroids, showing 20,851–20,900

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.925513111531✓all2rational
3.11.925523111514✓all2rational
3.11.925533111542✓all2rational
3.11.925563111532✓all2rational
3.11.925683111532✓all2rational
3.11.925693111532✓all2rational
3.11.925703111531✓all2rational
3.11.925723111521✓all2rational
3.11.925743111522✓all2rational
3.11.925753111521✓all2rational
3.11.925763111532✓all2rational
3.11.925773111522✓all2rational
3.11.925783111521✓all2rational
3.11.925793111522✓all2rational
3.11.925843111532✓all2rational
3.11.925853111532✓all2rational
3.11.925863111531✓all2rational
3.11.925873111532✓all2rational
3.11.925893111522✓all2rational
3.11.926083111522✓all2rational
3.11.926093111522✓all2rational
3.11.926103111521✓all2rational
3.11.926113111532✓all2rational
3.11.926123111521✓all2rational
3.11.926133111522✓all2rational
3.11.926173111522✓all2rational
3.11.926253111521✓all2rational
3.11.926313111511✓all2rational
3.11.926343111511✓all2rational
3.11.926363111511✓all2rational
3.11.927013111522✓all2rational
3.11.927933111511✓all2rational
3.11.927943111501✓all2rational
3.11.927953111501✓all2rational
3.11.927983111511✓all2rational
3.11.927993111511✓all2rational
3.11.928003111511✓all2rational
3.11.928023111501✓all2rational over Q(a)/(a^2 - a + 1)
3.11.928033111511✓all2rational
3.11.928093111512✓all2rational
3.11.928103111512✓all2rational
3.11.928113111502✓all2rational
3.11.928133111502✓all2rational
3.11.928143111504✓all2rational
3.11.928163111494✓all2rational
3.11.928563111521✓all2rational
3.11.928573111531✓all2rational
3.11.928593111521✓all2rational
3.11.928603111521✓all2rational
3.11.928613111521✓all2rational

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