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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.

8,076,768 matroids, showing 20,451–20,500

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.914423111521✓all2rational
3.11.914433111511✓all2rational
3.11.914443111511✓all2rational
3.11.914453111511✓all2rational
3.11.914463111511✓all2empty
3.11.914493111511✓all2rational
3.11.914543111531✓all2rational
3.11.914553111521✓all2rational
3.11.914563111521✓all2rational
3.11.914583111521✓all2rational
3.11.914593111521✓all2rational
3.11.914603111521✓all2rational
3.11.914613111511✓all2rational
3.11.914633111511✓all2rational
3.11.914643111521✓all2empty
3.11.914653111511✓all2empty
3.11.914663111511✓all2empty
3.11.914673111511✓all2empty
3.11.914703111511✓all2rational
3.11.914743111521✓all2empty
3.11.914783111511✓all2rational
3.11.914883111511✓all2rational
3.11.914973111521✓all2rational
3.11.915073111511✓all2rational
3.11.915083111521✓all2rational
3.11.915503111501✓all2rational
3.11.915513111501✓all2rational over Q(a)/(a^3 - a^2 + 1)
3.11.915523111511✓all2rational
3.11.915543111501✓all2rational
3.11.915553111501✓all2rational
3.11.915563111521✓all2rational
3.11.915683111511✓all2rational
3.11.915693111501✓all2rational
3.11.915703111501✓all2rational
3.11.915723111491✓all2empty
3.11.915733111521✓all2rational
3.11.915743111511✓all2rational
3.11.915823111501✓all2rational
3.11.915833111501✓all2empty
3.11.915843111491✓all2empty
3.11.915863111501✓all2empty
3.11.915873111501✓all2empty
3.11.915883111501✓all2rational
3.11.915993111521✓all2rational
3.11.916003111512✓all2empty
3.11.916013111521✓all2rational
3.11.916033111521✓all2rational
3.11.916043111511✓all2rational
3.11.916053111511✓all2rational
3.11.916073111511✓all2rational

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