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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.

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Invariants
Realizability
Properties

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5,849,183 matroids, showing 22,251–22,300

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.1847603111511✓all1rational
3.11.1847623111511✓all1rational
3.11.1847713111511✓all1rational
3.11.1847833111511✓all but 21rational
3.11.1847853111511✓all1rational
3.11.1847873111511✓all but 21rational
3.11.1847883111511✓all but 2,31rational
3.11.1847963111511✓all1rational
3.11.1847973111501✓all but 21rational
3.11.1847983111501✓all1rational
3.11.1847993111501✓all but 21rational
3.11.1852053111501✓all1rational
3.11.1852063111491✓all1rational
3.11.1852073111491✓all1rational
3.11.1852083111491✓all1rational
3.11.1852103111491✓all but 21rational
3.11.1852113111491✓all1rational
3.11.1852123111491✓all1rational
3.11.1852133111492✓all1rational
3.11.1852153111501✓all but 21rational
3.11.1852163111501✓all but 2,31rational
3.11.1852183111501✓all but 21rational
3.11.1852193111501✓all but 21rational
3.11.1852513111481✓all1rational
3.11.1852523111471✓all1rational
3.11.1852533111472✓all1rational
3.11.1852553111491✓all but 21rational
3.11.1852563111491✓all but 21rational
3.11.1852583111491✓all1rational
3.11.1852903111501✓all1rational
3.11.1852913111491✓all1rational
3.11.1852923111491✓all1rational
3.11.1852953111491✓all1rational
3.11.1852963111481✓all but 21rational
3.11.1852973111481✓all but 21rational
3.11.1852983111481✓all but 21rational
3.11.1854103111491✓all1rational
3.11.1854233111471✓all1rational
3.11.1854253111471✓all1rational
3.11.1854283111491✓all1rational
3.11.1854293111491✓all1rational
3.11.1854603111491✓all1rational
3.11.1854613111491✓all1rational
3.11.1854623111481✓all1rational
3.11.1854653111491✓all1rational
3.11.1854663111481✓all but 21rational
3.11.1854733111491✓all1rational
3.11.1854743111481✓all1rational
3.11.1854773111481✓all1rational
3.11.1854783111471✓all1point over Q(a)/(a^2 - 2)

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