New results on large sets of orthogonal arrays and orthogonal arrays

TL;DR

This paper introduces new series of large sets of orthogonal arrays through various construction methods, leading to many new infinite classes with applications in multiple scientific fields.

Contribution

It presents novel direct, juxtaposition, Hadamard, finite field, and difference matrix constructions for large sets of orthogonal arrays, expanding the known classes significantly.

Findings

New large sets of orthogonal arrays constructed

Infinite classes of orthogonal arrays obtained

Applications in statistics, coding theory, cryptography

Abstract

Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series of large sets of orthogonal arrays are given by direct construction, juxtaposition construction, Hadamard construction, finite field construction and difference matrix construction. Subsequently, many new infinite classes of orthogonal arrays are obtained by using these large sets of orthogonal arrays and Kronecker product.