Properties of Complete Sets of Mutually Equiorthogonal Frequency Hypercubes

A complete set of mutually equiorthogonal frequency hypercubes (MEFH) of ordern and dimensiond, usingm distinct symbols, has (n−1) d /(m−1) hypercubes. In this article, we explore the properties of complete sets of MEFH. As a consequence of these properties, we show that existence of such a set implies that the number of symbolsm is a prime power. We also establish an equivalence between existence of a complete set of MEFH and existence of a certain complete set of Latin hypercubes and a certain complete orthogonal array