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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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8,076,768 matroids, showing 20,351–20,400

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.911693111501✓all2rational
3.11.911703111501✓all2rational
3.11.911713111501✓all2rational
3.11.911733111501✓all2empty
3.11.911773111501✓all2empty
3.11.911783111501✓all2empty
3.11.911803111511✓all2rational
3.11.911823111511✓all2rational
3.11.911863111501✓all2rational
3.11.911873111491✓all2rational
3.11.911903111501✓all2rational
3.11.911923111501✓all2rational
3.11.911933111501✓all2rational
3.11.911943111511✓all2rational
3.11.911983111491✓all2point over Q(a)/(a^3 - a^2 + 1)
3.11.912033111491✓all2point over Q(a)/(a^4 - a^3 - a^2 + a + 1)
3.11.912063111491✓all2rational
3.11.912073111482✓all2rational
3.11.912083111481✓all2rational
3.11.912093111481✓all2rational
3.11.912143111501✓all2rational
3.11.912663111511✓all2rational
3.11.912673111511✓all2rational
3.11.912683111511✓all2rational
3.11.912693111511✓all2empty
3.11.912713111511✓all2rational
3.11.912723111501✓all2rational
3.11.912733111501✓all2rational
3.11.912753111501✓all2rational
3.11.912763111501✓all2rational
3.11.912773111521✓all2rational
3.11.912783111511✓all2rational
3.11.912803111511✓all2rational
3.11.912813111511✓all2rational
3.11.912823111511✓all2rational
3.11.912833111501✓all2rational
3.11.912853111511✓all2rational
3.11.912863111501✓all2rational
3.11.912873111501✓all2rational
3.11.912883111501✓all2rational over Q(a)/(a^2 + 1)
3.11.912903111491✓all2rational
3.11.912943111511✓all2rational
3.11.912953111511✓all2rational
3.11.912963111511✓all2rational
3.11.912993111511✓all2rational
3.11.913023111491✓all2rational
3.11.913063111511✓all2rational
3.11.913073111501✓all2rational
3.11.913083111501✓all2rational
3.11.913093111501✓all2rational

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