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MOLS

mutually orthogonal Latin squares

 Calling Sequence MOLS(p, m, n)

Parameters

 p - prime number m - positive integer n - positive integer less than p^m

Description

 • This function returns a list of n mutually orthogonal Latin squares of size p^m.
 • Two Latin squares, A and B, are mutually orthogonal if the set of ordered pairs $\left\{{A}_{i,j},{B}_{i,j},0\le i,j\le {p}^{m}\right\}$ has no repeated elements.

Examples

 > $\mathrm{MOLS}\left(3,1,2\right)$
 $\left[\left[\begin{array}{ccc}{0}& {1}& {2}\\ {1}& {2}& {0}\\ {2}& {0}& {1}\end{array}\right]{,}\left[\begin{array}{ccc}{0}& {1}& {2}\\ {2}& {0}& {1}\\ {1}& {2}& {0}\end{array}\right]\right]$ (1)