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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 21,001–21,050

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.931123111511✓all2rational
3.11.931133111511✓all2rational
3.11.931143111511✓all2rational
3.11.931153111511✓all2rational
3.11.931163111521✓all2rational
3.11.931213111511✓all2rational
3.11.931273111511✓all2rational
3.11.931283111511✓all2rational
3.11.931293111521✓all2rational
3.11.931303111511✓all2rational
3.11.931313111511✓all but 22rational
3.11.931353111511✓all2rational
3.11.931403111511✓all2rational
3.11.931453111501✓all2rational
3.11.931463111501✓all2rational
3.11.931473111511✓all2rational
3.11.931483111501✓all2rational
3.11.931493111501✓all but 22rational
3.11.931533111511✓all2rational
3.11.931573111501✓all2rational
3.11.931623111512✓all2empty
3.11.931643111502✓all2empty
3.11.931653111522✓all2rational
3.11.931663111511✓all2rational
3.11.931673111502✓all2rational
3.11.931713111501✓all2rational
3.11.931733111501✓all2rational
3.11.931743111501✓all2rational
3.11.931763111491✓all2point over Q(a)/(a^3 - a^2 + a + 1)
3.11.931773111491✓all2point over Q(a)/(a^2 - a + 1)
3.11.931793111541✓all2rational
3.11.931803111531✓all2rational
3.11.931813111531✓all2rational
3.11.931833111531✓all2rational
3.11.931843111531✓all but 22rational
3.11.931853111531✓all but 22rational
3.11.931873111531✓all2rational
3.11.931883111521✓all2rational
3.11.931893111521✓all2rational
3.11.931903111521✓all2rational
3.11.931913111521✓all2rational
3.11.932023111521✓all2rational
3.11.932033111521✓all2rational
3.11.932043111521✓all2rational
3.11.932053111531✓all2rational
3.11.932073111521✓all2rational
3.11.932083111521✓all2rational
3.11.932093111521✓all2rational
3.11.932113111521✓all2rational
3.11.932123111531✓all2rational

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