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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 18,651–18,700

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.18544093122051✓all7?
3.12.18544253122071✓all7?
3.12.18544353122061✓all7?
3.12.18545563122051✓all7?
3.12.18548103122061✓all7?
3.12.18552653122051✓all7?
3.12.18555103122051✓all7?
3.12.18559313122071✓all7?
3.12.18574883122061✓all7?
3.12.18581323122061✓all7?
3.12.18599193122071✓all7?
3.12.18615823122041✓all7?
3.12.18615843122061✓all7?
3.12.18616103122041✓all7?
3.12.18616183122051✓all7?
3.12.18616303122031✓all7?
3.12.18616363122051✓all7?
3.12.18616403122051✓all7?
3.12.18616433122071✓all7?
3.12.18617873122061✓all7?
3.12.18619853122061✓all7?
3.12.18621453122051✓all7?
3.12.18624253122071✓all7?
3.12.18630303122051✓all7?
3.12.18638063122051✓all7?
3.12.18640793122061✓all7?
3.12.18644963122071✓all7?
3.12.18653113122051✓all7?
3.12.18674623122071✓all7?
3.12.18690703122051✓all7?
3.12.18697653122061✓all7?
3.12.18699393122061✓all but 27?
3.12.18769083122041✓all7?
3.12.18786753122051✓all7?
3.12.18786773122051✓all7?
3.12.18787013122061✓all7?
3.12.18787093122051✓all7?
3.12.18787413122051✓all7?
3.12.18787453122041✓all7?
3.12.18787573122041✓all7?
3.12.18787853122061✓all7?
3.12.18787963122061✓all7?
3.12.18788513122071✓all7?
3.12.18788533122071✓all7?
3.12.18790053122061✓all7?
3.12.18792483122041✓all7?
3.12.18794493122051✓all7?
3.12.18795313122051✓all7?
3.12.18799453122051✓all7?
3.12.18810883122071✓all7?

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