Showing papers on "Orthogonal array published in 1977"
TL;DR: In this article, the existence of all Hadamard matrices of order 4t is proved via construction of a complete set of mutually orthogonal $F$-squares of order n = 4t, t being a positive integer.
Abstract: The purpose of this paper is to demonstrate the existence via construction of a complete set of mutually orthogonal $F$-squares of order $n = 4t, t$ a positive integer, with two distinct symbols. The proof assumes that all Hadamard matrices of order $4t$ exist; they are known to exist for all $1 \leqq t \leqq 50$ and for 2$^p$. Two methods of construction, that is, Hadamard matrix theory and factorial design theory, are given; the methods are related, but the approaches differ.
27 citations
TL;DR: In this paper, a class of orthogonal main-effect plans for 4.2 m experiments is constructed and the plans are saturated and provide orthogonality estimates of the mean and all main-effects when all interactions are assumed to be Lero.
Abstract: A class of orthogonal main-effect plans for 4.2 m experiments is constructed. These plans are saturated and provide orthogonal estimates of the mean and all main-effects when all interactions are assumed to be Lero.
21 citations
TL;DR: A general class of matrices, which are equivalent to orthogonal Latin squares, is used to construct a class of geodetic graphs of diameter two and the argument is reversed to prove a necessary condition for the existence of general classes of such graphs in terms of orthogonic Latin squares.
9 citations
TL;DR: In this paper, a short expository treatment of orthogonal partitions in general is given, based on the identification of a partition with a vector subspace of Euclidean $N$-space $R^N. This identification is not new as it is part of the usual vector space approach to analysis of variance.
Abstract: Finney has used orthogonal partitions in the context of the search for higher order (coarser) partitions of given Latin squares. Hedayat and Seiden use the term $F$-square to denote higher order partitions that are orthogonal to both rows and columns. This note is a short expository treatment of orthogonal partitions in general and is based on the identification of a partition with a vector subspace of Euclidean $N$-space $R^N$. This identification is not new as it is part of the usual vector space approach to analysis of variance. This approach puts the concept of orthogonal partitions in a simple light unencumbered by the language of design of experiments. Another advantage is that certain published bounds on the maximum number of orthogonal partitions of specified type are immediate from the dimensionality restriction imposed by $R^N$. In addition, some counting problems are identified which are of possible interest to researchers in design of experiments and combinatorics.
8 citations
01 Jan 1977
TL;DR: This paper uses circulant matrices, computer techniques and product designs to construct orthogonal designs in order 24.
Abstract: This paper uses circulant matrices, computer techniques and product designs to construct orthogonal designs in order 24.
8 citations
TL;DR: It is shown that N ( n )⩾7 for n > 4922, the maximum number of mutually orthogonal Latin squares of order n.
5 citations