Uniform random generation of Latin squares is a classical problem. In this paper we prove that both Latin squares and Sudoku designs are maximum cliques of properly defined graphs. We have developed a simple algorithm for uniform random sampling of Latin squares and Sudoku designs. The corresponding SAS code is available in the supplementary material.
"Random Latin squares and Sudoku designs generation." Electron. J. Statist. 8 (1) 883 - 893, 2014. https://doi.org/10.1214/14-EJS913