Large Sets of Orthogonal Arrays and Multimagic Squares

Large sets of orthogonal arrays (LOA) have been used to construct resilient functions and zigzag functions by D. R. Stinson. In this paper, a special kind of LOA, strong double large sets of orthogonal arrays (SDLOA), is introduced and some constructions are provided. Meanwhile, a construction of multimagic squares based on SDLOAs is also given. As its application, it is proved that a t‐multimagic square of order exists whenever q is a prime power and , , which improves a similar result by H. Derksen et al. from primes to prime powers in Amer. Math. Monthly (2007).