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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 22,551–22,600

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.35658423122051✓all7?
3.12.35658683122061✓all7?
3.12.35658883122071✓all7?
3.12.35659503122051✓all7?
3.12.35661903122051✓all7?
3.12.35663763122041✓all7?
3.12.35665163122081✓all7?
3.12.35669143122051✓all7?
3.12.35675863122071✓all7?
3.12.35683663122061✓all7?
3.12.35690263122051✓all7?
3.12.35725873122071✓all7?
3.12.35747433122061✓all but 27?
3.12.35760953122061✓all7?
3.12.35806563122061✓all7?
3.12.35845783122071✓all7?
3.12.35871623122061✓all7?
3.12.35894453122051✓all7?
3.12.35897973122041✓all7?
3.12.35987653122051✓all7?
3.12.35995533122051✓all7?
3.12.35995743122041✓all7?
3.12.35996203122041✓all7?
3.12.35996383122051✓all7?
3.12.35997253122051✓all7?
3.12.35997323122051✓all7?
3.12.35997523122041✓all7?
3.12.35997933122051✓all7?
3.12.36038453122061✓all7?
3.12.36052533122071✓all7?
3.12.36060303122061✓all7?
3.12.36060723122061✓all7?
3.12.36060933122081✓all7?
3.12.36061033122071✓all7?
3.12.36061463122071✓all7?
3.12.36061513122071✓all7?
3.12.36061633122061✓all7?
3.12.36062093122071✓all7?
3.12.36062193122071✓all7?
3.12.36062273122061✓all7?
3.12.36062333122061✓all7?
3.12.36063193122081✓all7?
3.12.36065593122071✓all7?
3.12.36069193122061✓all7?
3.12.36072763122071✓all7?
3.12.36079003122071✓all7?
3.12.36088153122061✓all7?
3.12.36114513122071✓all7?
3.12.36135323122081✓all7?
3.12.36156113122051✓all7?

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