Abstract
In the present paper we estimate how long it will take state-of-the-art combinatorial algorithms to enumerate all possible mutually orthogonal diagonal Latin squares of order 10. For this purpose we first evaluate the performance of DLX algorithm and contemporary algorithms for solving SAT in application to finding orthogonal mates of an arbitrary diagonal Latin square of order 10. Then we estimate the number of diagonal Latin squares of order 10 and use this information in combination with some techniques for exploiting symmetries and equivalences to approximate the amount of time it would take to process them using existing hardware.
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