New Covering Array Numbers

TL;DR

This paper introduces new covering array numbers by employing an optimized procedure to establish the minimal array sizes needed for specific combinatorial configurations, advancing the understanding of covering array existence.

Contribution

It provides new bounds for covering array numbers using an optimized construction method, improving previous results in combinatorial design theory.

Findings

New covering array numbers established for various parameters.

Optimized procedure reduces the size of covering arrays needed.

Enhanced bounds contribute to combinatorial design applications.

Abstract

A covering array CA(N; t; k; v) is an N x k array on v symbols such that every N x t subarray contains as a row each t-tuple over the v symbols at least once. The minimum N for which a CA(N; t; k; v) exists is called the covering array number of t, k, and v, and it is denoted by CAN(t; k; v). In this work we prove new CANs using an optimized procedure.