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On the existence of orthogonal arrays OA\((3,5,4n+2)\). (English) Zbl 1225.05051

Summary: By an OA\((3,5,v)\) we mean an orthogonal array (OA) of order \(v\), strength \(t=3\), index unity and 5 constraints. The existence of such an OA implies the existence of a pair of mutually orthogonal Latin squares (MOLSs) of side \(v\). After R. C. Bose, S. S. Shrikhande and E. T. Parker [Can. J. Math. 12, 189–203 (1960; Zbl 0093.31905)] disproved the long-standing Euler conjecture in 1960, one has good reason to believe that an OA\((3,5,4n+2)\) exists for any integer \(n \geqslant 2\). So far, however, no construction of an OA\((3,5,4n+2)\) for any value of \(n\) has been given. This paper tries to fill this gap in the literature by presenting an OA\((3,5,4n+2)\) for infinitely many values of \(n \geqslant 62\).

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares

Citations:

Zbl 0093.31905
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References:

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