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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 19,051–19,100

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.3659493122091✓all6?
3.12.3659553122091✓all6?
3.12.3659863122081✓all6?
3.12.3659973122091✓all6?
3.12.3660073122081✓all6?
3.12.3660253122091✓all6?
3.12.3661233122081✓all6?
3.12.3662183122091✓all6?
3.12.3662573122081✓all6?
3.12.3662603122081✓all6?
3.12.3662623122081✓all6?
3.12.3662893122081✓all6?
3.12.3662983122081✓all6?
3.12.3663533122071✓all6?
3.12.3664463122091✓all6?
3.12.3664793122081✓all6?
3.12.3665663122071✓all6?
3.12.3666033122081✓all6?
3.12.3666563122071✓all6?
3.12.3666613122081✓all6?
3.12.3666703122071✓all6?
3.12.3666873122081✓all6?
3.12.3667563122081✓all6?
3.12.3668033122071✓all6?
3.12.3668083122071✓all6?
3.12.3668143122081✓all6?
3.12.3668193122071✓all6?
3.12.3668353122081✓all6?
3.12.3668363122081✓all6?
3.12.3668473122071✓all6?
3.12.3668533122071✓all6?
3.12.3668543122071✓all6?
3.12.3668673122081✓all6?
3.12.3668693122071✓all6?
3.12.3668873122071✓all6?
3.12.3669223122071✓all6?
3.12.3669793122082✓all6?
3.12.3669963122071✓all6?
3.12.3670033122091✓all6?
3.12.3670073122081✓all6?
3.12.3670193122081✓all6?
3.12.3670343122071✓all6?
3.12.3670423122081✓all6?
3.12.3670513122081✓all6?
3.12.3672073122081✓all6?
3.12.3672203122081✓all6?
3.12.3672293122081✓all6?
3.12.3672343122081✓all6?
3.12.3672363122081✓all6?
3.12.3672383122081✓all6?

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