A family of multimagic squares based on large sets of orthogonal arrays

Large set of orthogonal arrays (LOA) were introduced by D. R. Stinson, and it is also used to construct multimagic squares recently. In this paper, multimagic squares based on strong double LOA are further investigated. It is proved that there exists an MS$(q^{2t-1},t)$ for any prime power $q\ge 2t-1$ with $t\ge 3$, which provided a new family of multimagic squares.