For a fully captured Latin square of order1..4 on labels0..n-1, construct ALL La...
https://datenvertrag.halowerk.com/v1/latin-square-orthogonal-mate-familyOverview
For a fully captured Latin square of order1..4 on labels0..n-1, construct ALL Latin squares B for which every ordered pair (original[r][c],B[r][c]) occurs exactly once. Return every mate as a flat row-major value array in numeric lexicographic order, aligned pair_codes[r*n+c]=n*original[r][c]+B[r][c], and count. Retain every symbol-labelled mate; no symmetry quotient. A valid square without mates has a known empty family. n1 admits its single square as its mate.