SAT-based search for systems of diagonal latin squares in volunteer computing project SAT@home

In this paper we considered the problem of finding pairs of mutually orthogonal diagonal Latin squares of order 10. First we reduced it to Boolean satisfiability problem. The obtained instance is very hard, therefore we decomposed it into a family of subproblems. To solve the latter we used the volunteer computing project SAT@home. In the course of 10-month long computational experiment we managed to find 29 pairs of described kind, that are different from already known pairs. Also we considered the problem of search for triples of diagonal Latin squares of order 10 that satisfy weakened orthogonality condition. Using diagonal Latin squares from the known pairs (the most of them were found in SAT@home) we constructed new triples of proposed kind. During this computational experiment we used a computing cluster.