The Search for Systems of Diagonal Latin Squares Using the SAT@home Project

In this paper we consider the approach to solving the problem of search for systems of diagonal orthogonal Latin squares in the form of the Boolean Satisfiability problem. We describe two different propositional encodings that we use. The first encoding is constructed for finding pairs of orthogonal diagonal Latin squares of order 10. Using this encoding we managed to find 17 previously unknown pairs of such squares using the volunteer computing project SAT@home. The second encoding is constructed for finding pseudotriples of orthogonal diagonal Latin squares of order 10. Using the pairs found with the help of SAT@home and the second encoding we successfully constructed several new pseudotriples of diagonal Latin squares of order 10.