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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 22,351–22,400

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.12.4445103122071✓all6?
3.12.4445113122071✓all6?
3.12.4445233122061✓all6?
3.12.4445553122061✓all6?
3.12.4445563122061✓all6?
3.12.4445683122081✓all6?
3.12.4445823122071✓all6?
3.12.4445863122061✓all6?
3.12.4445903122071✓all6?
3.12.4446043122071✓all6?
3.12.4446213122091✓all6?
3.12.4446553122081✓all6?
3.12.4446673122081✓all6?
3.12.4446913122081✓all6?
3.12.4447223122081✓all6?
3.12.4447923122071✓all6?
3.12.4448603122081✓all6?
3.12.4450103122071✓all6?
3.12.4450323122071✓all6?
3.12.4450723122061✓all6?
3.12.4450803122071✓all6?
3.12.4450813122071✓all6?
3.12.4450983122081✓all6?
3.12.4451023122081✓all6?
3.12.4451123122071✓all6?
3.12.4451153122071✓all6?
3.12.4451673122071✓all6?
3.12.4451813122071✓all6?
3.12.4451843122071✓all6?
3.12.4452673122091✓all6?
3.12.4452773122101✓all6?
3.12.4453283122081✓all6?
3.12.4453723122091✓all6?
3.12.4454713122081✓all6?
3.12.4456793122081✓all6?
3.12.4457413122081✓all6?
3.12.4457573122081✓all6?
3.12.4457663122091✓all6?
3.12.4457873122071✓all6?
3.12.4459113122081✓all6?
3.12.4459503122081✓all6?
3.12.4459693122071✓all6?
3.12.4459923122071✓all6?
3.12.4459983122081✓all6?
3.12.4460853122081✓all6?
3.12.4460933122081✓all6?
3.12.4461473122091✓all6?
3.12.4462113122081✓all6?
3.12.4462363122071✓all6?
3.12.4463143122061✓all6?

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