Determining Covering Array Numbers via Balanced Covering Arrays

Abstract: In this article we determine five previously unknown covering array numbers (CANs). We do so using properties of so called balanced covering arrays together with a computational result for these. The balance properties allow us to generalize the (computational) non-existence result for balanced covering arrays to covering arrays. Covering arrays are combinatorial designs that can be considered generalizations of orthogonal arrays, when dropping the restriction that the considered $t$-tuples appear exactly $\lambda$ times, and instead require them to appear at least $\lambda$ times. While this generalization renders the existence of covering arrays trivial, it raises the question for their optimality, respectively the smallest number of rows, the CAN, for which a certain covering array exists. The CANs determined in this paper were tightly bound for decades, but remained ultimately unknown.