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).