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…or describe it by its bases, non-bases or lines

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.

8,076,768 matroids, showing 21,051–21,100

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.932133111521✓all2rational
3.11.932143111521✓all2rational
3.11.932163111521✓all2rational
3.11.932173111521✓all2rational
3.11.932183111521✓all2rational
3.11.932203111511✓all2rational
3.11.932213111511✓all2rational
3.11.932223111521✓all2rational
3.11.932233111511✓all2rational
3.11.932253111511✓all2rational
3.11.932293111521✓all2rational
3.11.932303111521✓all2rational
3.11.932323111521✓all but 22rational
3.11.932343111511✓all2rational
3.11.932373111521✓all2rational
3.11.932413111521✓all2rational
3.11.932433111511✓all2rational
3.11.932443111511✓all2rational
3.11.932453111511✓all2rational
3.11.932493111521✓all2rational
3.11.932543111511✓all2rational
3.11.932563111521✓all but 22rational
3.11.932583111511✓all but 22rational
3.11.932603111521✓all but 22rational
3.11.932623111511✓all but 22empty
3.11.932763111521✓all2rational
3.11.932773111521✓all2rational
3.11.932783111521✓all2rational
3.11.932793111511✓all2rational
3.11.932813111511✓all2rational
3.11.932823111521✓all2rational
3.11.932833111511✓all2rational
3.11.932853111511✓all2rational
3.11.932863111521✓all2rational
3.11.932873111511✓all2rational
3.11.932883111511✓all2rational
3.11.932903111511✓all2rational
3.11.932913111501✓all2rational
3.11.932923111521✓all2rational
3.11.932943111511✓all2rational
3.11.932953111511✓all2rational
3.11.932963111511✓all2rational
3.11.932973111501✓all2rational
3.11.932993111522✓all2rational
3.11.933043111531✓all2rational
3.11.933053111521✓all2rational
3.11.933063111521✓all but 22rational
3.11.933083111511✓all2rational
3.11.933113111521✓all2rational
3.11.933163111521✓all2rational

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