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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
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8,076,768 matroids, showing 21,151–21,200

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.934723111511✓all2rational
3.11.934743111511✓all2rational
3.11.934763111521✓all2rational
3.11.934853111511✓all2rational
3.11.934863111501✓all2rational
3.11.934873111511✓all2rational
3.11.934883111501✓all2genus 1 curve (11a3)
3.11.934903111511✓all2rational
3.11.934913111501✓all2rational
3.11.934923111501✓all2rational
3.11.934933111521✓all2rational
3.11.934953111511✓all2rational
3.11.934973111511✓all2rational
3.11.934983111501✓all2rational
3.11.934993111511✓all2rational
3.11.935013111501✓all2rational
3.11.935023111511✓all2rational
3.11.935033111501✓all2rational
3.11.935043111501✓all2empty
3.11.935053111501✓all2rational
3.11.935093111491✓all2rational
3.11.935153111511✓all2rational
3.11.935163111511✓all2rational
3.11.935173111501✓all2genus 1 curve (14a4)
3.11.935183111501✓all2rational
3.11.935193111501✓all but 22rational
3.11.935233111511✓all2rational
3.11.935273111511✓all2rational
3.11.935333111511✓all2rational
3.11.935353111511✓all2rational
3.11.935363111511✓all2rational
3.11.935373111501✓all but 22rational
3.11.935413111501✓all2rational
3.11.935473111511✓all2rational
3.11.935513111522✓all2rational
3.11.935533111502✓all2empty
3.11.935543111511✓all2rational
3.11.935553111501✓all2rational
3.11.935563111511✓all2rational
3.11.935573111501✓all2rational
3.11.935603111481✓all2rational
3.11.935653111491✓all2point over Q(a)/(a^2 - a + 2)
3.11.935713111511✓all2rational
3.11.935723111501✓all2rational
3.11.935733111501✓all2rational
3.11.935743111501✓all2rational
3.11.935763111491✓all2rational
3.11.935773111531✓all2rational
3.11.935793111521✓all2rational
3.11.935863111511✓all but 22rational

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