On Construction of a Class of Orthogonal Arrays (Thesis)

TL;DR

This thesis introduces a new algorithm leveraging the Kronecker Product to construct orthogonal arrays from existing ones, applicable to any linear seed array without constraints, producing arrays with the same strength.

Contribution

It presents a novel, general method for constructing orthogonal arrays using Kronecker products, expanding the available array library without restrictions on seed arrays.

Findings

Generated new orthogonal arrays not in existing libraries

Algorithm works with any linear seed array

Maintains the strength of the seed array

Abstract

We propose a novel method for the construction of orthogonal arrays. The algorithm makes use of the Kronecker Product operator in association with unit column vectors to generate new orthogonal arrays from existing orthogonal arrays. The effectiveness of the proposed algorithm lies in the fact that it works well with any linear seed orthogonal array without imposing any constraints on the strength or the number of levels. The resulting orthogonal array has the same strength as the seed orthogonal array. We also discuss the proof of correctness of the algorithm. In the Results section we provide a list of new orthogonal arrays generated using this algorithm, that are currently not present in the libraries of orthogonal arrays.