Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Constructing ordered orthogonal arrays via sudoku

For prime powers [Formula: see text] we use “strongly orthogonal” linear sudoku solutions of order [Formula: see text] to construct ordered orthogonal arrays of type [Formula: see text], and for each [Formula: see text] we present a range of values of [Formula: see text] for which these constructions are valid. These results rely strongly on flags of subspaces in a four-dimensional vector space over a finite field.

A Generalized Rao Bound for Ordered Orthogonal Arrays and (t, m, s)-Nets

In this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and (t, m, s)-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (i.e., necessary conditions) for existence of these objects.

Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets

In an earlier paper [10], we studied a generalized Rao bound for ordered orthogonal arrays and (T, M, S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We include some tables which compare this bound against two previously known bounds for ordered orthogonal arrays. Finally we show that, for even strength, the LP bound is always at least as strong as the generalized Rao bound.