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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.

381,906 matroids, showing 22,551–22,600

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.4494453122081✓all6?
3.12.4494553122071✓all6?
3.12.4494713122071✓all6?
3.12.4494853122081✓all6?
3.12.4494953122071✓all6?
3.12.4495343122081✓all6?
3.12.4495923122081✓all6?
3.12.4496533122071✓all6?
3.12.4496893122081✓all6?
3.12.4497803122071✓all6?
3.12.4498333122081✓all6?
3.12.4498823122091✓all6?
3.12.4499273122071✓all6?
3.12.4499283122071✓all6?
3.12.4499393122071✓all6?
3.12.4499463122071✓all6?
3.12.4499493122071✓all6?
3.12.4499623122071✓all6?
3.12.4499673122071✓all6?
3.12.4499693122071✓all6?
3.12.4499883122071✓all6?
3.12.4500383122081✓all6?
3.12.4500443122081✓all6?
3.12.4500703122081✓all6?
3.12.4500743122071✓all6?
3.12.4501283122081✓all6?
3.12.4501483122081✓all6?
3.12.4502263122071✓all6?
3.12.4502343122071✓all6?
3.12.4502563122071✓all6?
3.12.4502713122091✓all6?
3.12.4502943122071✓all6?
3.12.4503043122071✓all6?
3.12.4503093122081✓all6?
3.12.4503133122071✓all6?
3.12.4503393122071✓all6?
3.12.4503493122071✓all6?
3.12.4503643122071✓all6?
3.12.4503793122071✓all6?
3.12.4503803122071✓all6?
3.12.4504563122061✓all6?
3.12.4504743122061✓all6?
3.12.4505043122081✓all6?
3.12.4505343122081✓all6?
3.12.4505663122081✓all6?
3.12.4505693122081✓all6?
3.12.4505723122081✓all6?
3.12.4505773122071✓all6?
3.12.4505793122071✓all6?
3.12.4506043122081✓all6?

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