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Complete Sets of Mutually Orthogonal Hypercubes and Their Connections to Affine Resolvable Designs
Ilene H. Morgan
Department of Mathematics and Statistics, University of Missouri-Rolla Rolla, MO 65409-0020, USA
imorgan@umr.edu
Annals of Combinatorics 5 (2) p.227-240 June, 2001
AMS Subject Classification: 05B30
Abstract:
Recently, Laywine and Mullen proved several generalizations of Bose's equivalence between the existence of complete sets of mutually orthogonal Latin squares of order n and the existence of affine planes of order n. Laywine further investigated the relationship between sets of orthogonal frequency squares and affine resolvable balanced incomplete block designs. In this paper we generalize several of Laywine's results that were derived for frequency squares. We provide sufficient conditions for construction of an affine resolvable design from a complete set of mutually orthogonal Youden frequency hypercubes; we also show that, starting with a complete set of mutually equiorthogonal frequency hypercubes, an analogous construction can always be done. In addition, we give conditions under which an affine resolvable design can be converted to a complete set of mutually orthogonal Youden frequency hypercubes or a complete set of mutually equiorthogonal frequency hypercubes.
Keywords: frequency hypercubes, affine resolvable balanced incomplete block designs, prime blocks

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