Covering arrays of strength 3 and 4 from holey difference matrices

Abstract

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 × t sub-array contains all t-tuples over X at least once, where t is the strength of the array. The minimum size N for which a CA(N ; t, k, v) exists is called the covering array number and denoted by CAN(t, k, v). Covering arrays are used in experiments to screen for interactions among t-subsets of k components. One of the main problems on covering arrays is to construct a CA(N ; t, k, v) for given parameters (t, k, v) so that N is as small as possible. In this paper, we present some constructions of covering arrays of strengths 3 and 4 via holey difference matrices with prescribed properties. As a consequence, some of known bounds on covering array number are improved. In particular, it is proved that (1) CAN(3, 5, 2v) ≤ 2v 2 (4v + 1) for any odd positive integer v with gcd(v, 9) = 3; (2) CAN

Constructions of covering arrays of strength five

“…If 1 = G\H , then this HDM is denoted by (4, v; w)-HDM * as in [15]. If 1 = 2 = 3 = G\H , then this HDM is denoted by (4, v; w)-HDM * * .…”

“…It is beyond of this paper to give a survey. For detailed information and related results, the reader is refer to recent papers [5,[7][8][9]14,15,17] and references therein.…”

Asymptotic Size of Covering Arrays: An Application of Entropy Compression

“…In , there is a constructive method for finding covering arrays of logarithmic size for any , but only when k is a prime power that satisfies certain constraints. Some constructions rely on finite fields to produce infinite families of covering arrays with for which k and v are certain functions of a prime power , or with , and v being a specific function of a prime . None of these results give a fully general upper bound on .…”

Recursive constructions for covering schemes of strength 3

“…Cyclic groups play a central role in the study of several types of difference arrays (see [2,8,9,10,14,20,30,31] for instance). The same phenomenon happens for covering schemes.…”

“…Many orthogonal arrays induced by MDS codes are not invariant; see [3]. The covering arrays in Theorem 2.2 of [20] are not invariant, according to Proposition 6.7. See also Proposition 6.8.…”