Geodesic
Applying high-performance computing to searching for triples of partially orthogonal Latin squares of order 10
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 3, pp. 54-89

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This paper deals with the search for triples of partially orthogonal Latin squares of order 10. For every known pair of orthogonal Latin squares of order 10 we add a third diagonal Latin square in such a way that the orthogonality condition between it and squares from a considered pair coincides in the maximum possible number of cells. Two approaches are used: the first one is based on reducing an original problem to Boolean satisfiability problem; the second one is based on Brute force method. Several triples of the aforementioned kind with high characteristics were constructed. The experiments were held in the volunteer computing project SAT@home and on a computing cluster.
Keywords: diagonal Latin squares, partial orthogonality, Boolean satisfiability problem, volunteer computing, computing cluster.
Mots-clés : brute force 
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     title = {Applying high-performance computing to searching for triples of partially orthogonal {Latin} squares of order 10},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
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O. S. Zaikin; E. I. Vatutin; A. D. Zhuravlev; M. O. Manzyuk. Applying high-performance computing to searching for triples of partially orthogonal Latin squares of order 10. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 3, pp. 54-89. http://geodesic.mathdoc.fr/item/VYURV_2016_5_3_a3/