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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 18,351–18,400

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.17222403122061✓all7?
3.12.17222483122061✓all7?
3.12.17222573122071✓all7?
3.12.17222773122081✓all7?
3.12.17222783122071✓all7?
3.12.17222843122061✓all7?
3.12.17223103122061✓all7?
3.12.17223283122061✓all7?
3.12.17224483122061✓all7?
3.12.17225033122051✓all7?
3.12.17225733122051✓all7?
3.12.17227173122051✓all7?
3.12.17229233122071✓all7?
3.12.17230983122061✓all7?
3.12.17231843122061✓all7?
3.12.17234993122071✓all7?
3.12.17239723122061✓all7?
3.12.17245003122071✓all7?
3.12.17247963122061✓all7?
3.12.17252293122071✓all7?
3.12.17265143122071✓all7?
3.12.17281693122061✓all7?
3.12.17285813122051✓all7?
3.12.17292453122051✓all7?
3.12.17294163122051✓all7?
3.12.17305803122061✓all7?
3.12.17325593122051✓all7?
3.12.17325693122051✓all7?
3.12.17325873122061✓all7?
3.12.17326063122081✓all7?
3.12.17326123122071✓all7?
3.12.17326143122071✓all7?
3.12.17326223122061✓all7?
3.12.17326313122071✓all7?
3.12.17326523122061✓all7?
3.12.17327343122071✓all7?
3.12.17328173122071✓all7?
3.12.17329003122061✓all7?
3.12.17329593122071✓all7?
3.12.17330863122071✓all7?
3.12.17332013122061✓all7?
3.12.17333243122071✓all7?
3.12.17338013122071✓all7?
3.12.17342323122051✓all7?
3.12.17347813122061✓all7?
3.12.17350873122061✓all7?
3.12.17355953122061✓all7?
3.12.17362013122061✓all7?
3.12.17383803122071✓all7?
3.12.17403723122061✓all7?

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