Mixed covering arrays of strength three with few factors

Covering arrays with mixed alphabet sizes, or mixed covering arrays, are useful generalizations of covering arrays that are motivated by software and network testing. Suppose that there are k factors, and that the ith factor takes values or levels from a set G_i of size g_i. A run is an assignment of an admissible level to each factor. A mixed covering array, MCA(N;t,k,g₁g₂...g_k), is a collection of N runs such that for any t distinct factors, i₁,i₂,...,i_t, every t-tuple from G_i1×G_i2×. .×G_it occurs in factors i₁,i₂,...,i_t in at least one of the N runs. When g=g₁=g₂=...=g_k, an MCA(N;t,k,g₁g₂...g_k) is a CA(N;t,k,g). The mixed covering array number, denoted by MCAN(t,k,g1g2...gk), is the minimum N for which an MCA(N;t,k,g₁g₂...g_k) exists. In this paper, we focus on the constructions of mixed covering arrays of strength three. The numbers MCAN(3,k,g₁g₂...g_k) are determined for all cases with k∈{3,4} and for most cases with k∈;{5,6}.