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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 18,651–18,700

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.3535713122081✓all6?
3.12.3535873122081✓all6?
3.12.3535883122071✓all6?
3.12.3535903122071✓all6?
3.12.3536053122071✓all6?
3.12.3536113122081✓all6?
3.12.3536133122081✓all6?
3.12.3536453122091✓all6?
3.12.3536923122071✓all6?
3.12.3537243122071✓all6?
3.12.3537353122101✓all6?
3.12.3537463122091✓all6?
3.12.3537713122091✓all6?
3.12.3537783122091✓all6?
3.12.3538243122091✓all6?
3.12.3538413122081✓all6?
3.12.3538503122091✓all6?
3.12.3538543122091✓all6?
3.12.3539143122081✓all6?
3.12.3539553122091✓all6?
3.12.3539603122081✓all6?
3.12.3539843122081✓all6?
3.12.3540383122081✓all6?
3.12.3540643122081✓all6?
3.12.3540763122091✓all6?
3.12.3540903122071✓all6?
3.12.3540983122081✓all6?
3.12.3541033122071✓all6?
3.12.3541053122081✓all6?
3.12.3541283122071✓all6?
3.12.3541393122091✓all6?
3.12.3541433122081✓all6?
3.12.3541603122071✓all6?
3.12.3541613122091✓all6?
3.12.3541873122071✓all6?
3.12.3541913122081✓all6?
3.12.3541983122071✓all6?
3.12.3542073122081✓all6?
3.12.3542143122091✓all6?
3.12.3542853122071✓all6?
3.12.3542963122081✓all6?
3.12.3543073122081✓all6?
3.12.3543153122081✓all6?
3.12.3543293122091✓all6?
3.12.3543423122081✓all6?
3.12.3543753122081✓all6?
3.12.3543823122091✓all6?
3.12.3544013122081✓all6?
3.12.3544853122081✓all6?
3.12.3545033122081✓all6?

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