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

TL;DR

This paper explores the construction of multimagic squares using strong double large sets of orthogonal arrays, establishing new existence results for these squares based on prime power parameters.

Contribution

It introduces a new family of multimagic squares derived from strong double LOA, expanding the known existence conditions for such squares.

Findings

Existence of MS(q^{2t-1},t) for prime powers q ≥ 2t-1 with t ≥ 3.

New construction method for multimagic squares using strong double LOA.

Extension of previous results on multimagic squares based on orthogonal arrays.

Abstract

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 $q\geq 2t-1$ with $t\geq3$, which provided a new family of multimagic squares.