Constructions for mutually orthogonal frequency hyperrectangles with a prescribed type Original Research Article

In this paper, we give two different ways to construct mutually orthogonal frequency hyperrectangles (MOFHR). Firstly, we exhibit sets of linear polynomials over finite fields that represent complete sets of MOFHR of prime power order, which generalize Mullenʹs method in (G.L. Mullen, Discrete Math. 69 (1988) 79–84). Secondly, a recursive algorithm is given to construct (d+1)-dimensional MOFHR of type t+1 from d-dimensional MOFHR of type t, which generalizes a recursive procedure described in (Laywine et al., Monatsch Math. 119 (1995) 223–238).