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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.

84,161 matroids, showing 18,951–19,000

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.19453903122071✓all7?
3.12.19454253122061✓all7?
3.12.19454713122061✓all7?
3.12.19455393122071✓all7?
3.12.19455453122071✓all7?
3.12.19455603122071✓all7?
3.12.19456453122061✓all7?
3.12.19457763122061✓all7?
3.12.19458863122051✓all7?
3.12.19458953122061✓all7?
3.12.19459163122051✓all7?
3.12.19459333122061✓all7?
3.12.19459473122071✓all7?
3.12.19459523122061✓all7?
3.12.19459803122051✓all7?
3.12.19460243122061✓all7?
3.12.19460413122071✓all7?
3.12.19462893122071✓all7?
3.12.19463513122081✓all7?
3.12.19464033122071✓all7?
3.12.19464543122081✓all7?
3.12.19464583122081✓all7?
3.12.19464603122071✓all7?
3.12.19464713122081✓all7?
3.12.19464723122071✓all7?
3.12.19464843122071✓all7?
3.12.19464863122071✓all7?
3.12.19464983122071✓all7?
3.12.19465073122061✓all7?
3.12.19465713122061✓all7?
3.12.19466993122081✓all7?
3.12.19468283122071✓all7?
3.12.19468933122061✓all7?
3.12.19470653122061✓all7?
3.12.19470813122071✓all7?
3.12.19470833122071✓all7?
3.12.19470853122061✓all7?
3.12.19470963122071✓all7?
3.12.19471133122061✓all7?
3.12.19471193122071✓all7?
3.12.19471383122071✓all7?
3.12.19471563122051✓all7?
3.12.19473093122061✓all7?
3.12.19473733122071✓all7?
3.12.19474923122071✓all7?
3.12.19475843122071✓all7?
3.12.19477083122061✓all7?
3.12.19479163122061✓all7?
3.12.19479383122051✓all7?
3.12.19479473122061✓all7?

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