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…or describe it by its bases, non-bases or lines
Matroid

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.

Size
Invariants
Realizability
Properties

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1,370,992 matroids, showing 19,401–19,450

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.2634003111392✗all5rational
3.11.2634093111384✗all5rational
3.11.2634123111384✗all5rational
3.11.2634233111382✗all5rational
3.11.2634243111362✗all5rational
3.11.2634293111358✗all5rational
3.11.2634303111368✗all5empty
3.11.26343331112816✗all5rational
3.11.2634503111392✗all5rational
3.11.2634763111378✗all5rational
3.11.2634833111382✗all5rational
3.11.2635023111372✗all5rational
3.11.2635053111372✗all5rational
3.11.2635213111378✗all5rational
3.11.2635233111388✗all5rational
3.11.2635263111372✗all5rational
3.11.2635493111372✗all5rational
3.11.2635613111372✗all5rational
3.11.2635673111362✗all5rational
3.11.2635733111364✗all5rational
3.11.2635743111364✗all5rational
3.11.2635783111384✗all5rational
3.11.2635853111372✗all5rational
3.11.2635893111342✗all5rational
3.11.2635903111342✗all5rational
3.11.2635913111372✗all5rational
3.11.2635943111362✗all5rational
3.11.2635953111362✗all5rational
3.11.2636043111354✗all5rational
3.11.26361431113412✗all5rational
3.11.2636193111384✗all but 25rational
3.11.2636513111372✗all5rational
3.11.2636583111362✗all5rational
3.11.2637653111334✗all5rational
3.11.2637773111344✗all5rational
3.11.2637793111322✗all5rational
3.11.2637903111364✗all5empty
3.11.2637933111334✗all5empty
3.11.26382931114696✗all5rational
3.11.2638543111448✗all5rational
3.11.2638613111448✗all5rational
3.11.26387431114312✗all5rational
3.11.26387831114324✗all5rational
3.11.2638813111444✗all5rational
3.11.2638933111468✗all5rational
3.11.2639013111444✗all5rational
3.11.2639063111444✗all5rational
3.11.2639573111432✗all5rational
3.11.2639683111444✗all5rational
3.11.26398531114212✗all5empty

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