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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 21,201–21,250

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.935883111521✓all but 22rational
3.11.935893111511✓all but 22rational
3.11.935913111511✓all but 22rational
3.11.935923111521✓all but 22rational
3.11.935933111511✓all but 22rational
3.11.935953111511✓all but 22rational
3.11.935963111521✓all but 22rational
3.11.935973111511✓all but 22rational
3.11.935993111511✓all but 22rational
3.11.936003111511✓all but 22rational
3.11.936013111521✓all but 22rational
3.11.936023111511✓all but 22rational
3.11.936053111511✓all but 22rational
3.11.936063111501✓all but 22rational
3.11.936083111501✓all but 22rational
3.11.936123111511✓all but 22rational
3.11.936133111511✓all but 22empty
3.11.936143111511✓all but 22rational
3.11.936153111501✓all but 22rational over Q(a)/(a^3 - a^2 + a + 1)
3.11.936163111511✓all but 22rational
3.11.936273111511✓all2rational
3.11.936283111511✓all2rational
3.11.936293111511✓all2rational
3.11.936303111501✓all2rational
3.11.936323111511✓all2rational
3.11.936333111501✓all2rational
3.11.936343111511✓all2rational
3.11.936363111501✓all2empty
3.11.936373111501✓all2rational
3.11.936383111521✓all2rational
3.11.936393111511✓all2rational
3.11.936413111511✓all2rational
3.11.936423111511✓all2rational
3.11.936433111511✓all2rational
3.11.936443111501✓all2empty
3.11.936463111501✓all2rational over Q(a)/(a^3 - a^2 + 1)
3.11.936473111511✓all2rational
3.11.936483111501✓all2rational
3.11.936493111501✓all but 22rational over Q(a)/(a^3 - a^2 + a + 1)
3.11.936513111501✓all2rational
3.11.936543111512✓all2empty
3.11.936583111511✓all2rational
3.11.936593111511✓all2rational
3.11.936603111501✓all2rational
3.11.936613111511✓all but 22rational
3.11.936633111522✓all2rational over Q(a)/(a^2 + 1)
3.11.936663111511✓all2rational over Q(a)/(a^2 + 1)
3.11.936703111492✓all2rational over Q(a)/(a^2 + 1)
3.11.936713111482✓all2rational over Q(a)/(a^2 + 1)
3.11.936723111511✓all2rational over Q(a)/(a^2 + 1)

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