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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 19,651–19,700

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.3787003122081✓all6?
3.12.3787103122081✓all6?
3.12.3787113122081✓all6?
3.12.3787593122081✓all6?
3.12.3788043122081✓all6?
3.12.3788403122081✓all6?
3.12.3788733122071✓all6?
3.12.3788943122081✓all6?
3.12.3789213122071✓all6?
3.12.3791593122071✓all6?
3.12.3791743122061✓all6?
3.12.3791893122071✓all6?
3.12.3791973122081✓all6?
3.12.3792013122071✓all6?
3.12.3792503122101✓all6?
3.12.3792773122091✓all6?
3.12.3792883122071✓all6?
3.12.3792933122071✓all6?
3.12.3793313122071✓all6?
3.12.3793443122091✓all6?
3.12.3793733122071✓all6?
3.12.3793933122081✓all6?
3.12.3794083122071✓all6?
3.12.3794143122081✓all6?
3.12.3794213122061✓all6?
3.12.3794353122071✓all6?
3.12.3794443122081✓all6?
3.12.3794973122071✓all6?
3.12.3795103122071✓all6?
3.12.3795303122071✓all6?
3.12.3795753122081✓all6?
3.12.3796193122081✓all6?
3.12.3796453122081✓all6?
3.12.3796983122062✓all6?
3.12.3797783122081✓all6?
3.12.3798003122081✓all6?
3.12.3798023122081✓all6?
3.12.3798223122081✓all6?
3.12.3798233122081✓all6?
3.12.3798333122081✓all6?
3.12.3798483122081✓all6?
3.12.3798533122091✓all6?
3.12.3798583122091✓all6?
3.12.3798993122081✓all6?
3.12.3799223122081✓all6?
3.12.3799423122071✓all6?
3.12.3799513122071✓all6?
3.12.3799703122081✓all6?
3.12.3800013122081✓all6?
3.12.3800813122081✓all6?

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