Constructions of covering arrays of strength five

A covering array of size N, strength t, degree k and order v, or a CA(N; t, k, v) in short, is an N x k array on v symbols. In every N x t subarray, each t-tuple occurs in at least one row. Covering arrays have been studied for their significant applications to generating software test suites to cover all t-sets of component interactions. In this paper, we present two constructive methods to obtain covering arrays of strength 5 by using difference covering arrays and holey difference matrices with a prescribed property. As a consequence, some new upper bounds on the covering numbers are derived.