Constructions Of Covering Arrays With Strength From Four To Eight

A covering array CA(N; t, k, v) is an N×k array with entries from a set X of v symbols such that every N x t sub-array contains all t-tuples over X at least once. Then t is the strength of the coverage of interactions, k is the number of components, and v is the number of symbols for each component. When'at least'is replaced by'exactly' this defines an orthogonal array. The minimum size N for which a CA(N; t, k, v) exists is called the covering array number and written as CAN(t, k, v).Covering arrays have a number of applications in experimental design, for example in software testing, in data compressing and in drug screening. Covering arrays for strength t= 2, in particular orthogonal arrays,have been extensively studied. However, very little is known about covering arrays for strength t≥3.In this paper, we present some constructions of covering arrays of strengths from four to eight via difference covering arrays with prescribed properties. Some difference covering arrays of theoretical constructions and direct constructions are presented as well in this paper. Our constructions of covering arrays improved the upper bounds of some covering array numbers significantly. At last, we present a construction of covering arrays of strength four via holey difference matrices with prescribed properties.