Improved Strength Four Covering Arrays with Three Symbols

Abstract

A covering array t-CA(n, k, g), of size n, strength t, degree k, and order g, is a 𝑘×𝑛 array on g symbols such that every 𝑡×𝑛 sub-array contains every 𝑡×1 column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we present an algebraic construction that improves many of the best known upper bounds on n for covering arrays 4-CA(n, k, 3). The t-coverage of a testing array 𝒜 is the number of distinct t-tuples contained in the column vectors of 𝒜 divided by the total number of t-tuples. If the testing array is a covering array of strength t, its t-coverage is 100%. The covering arrays with budget constraints problem is the problem of constructing a testing array of size at most n having largest possible coverage, given values of t, k, g and n. This paper also presents several testing arrays with high 4-coverage.