Covering Arrays Of Strength 3

Covering array is an important object in combinatorial designs and experimental designs.A covering array CAλ(N; t, k,v) is an N × k array with entries from a set V of v symbols such that every N x t sub-array contains all t-tuples over V at least A times. Then N is called the size (block number) of covering array, t is called the strength, k(k≥ t) is called the degree, v is called the levels and λ is called the index. When "at least" is replaced by "exactly", covering array is defined as an orthogonal array denoted by OAλ(t,k,v). 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). If N= CAN(t,k,v), then the CA(N;t,k,v) is called optimal.Covering arrays are mainly applied in data compressing, software testing, drug screening and some other experimental designs. Covering arrays of strength two, es-pecially orthogonal arrays have been investigated widely. In recent years, covering arrays of strength three have become the concern of many scholars, but the study has not been made of abundant achievements.In this paper, some new construction methods of covering arrays of strength three are given. The upper bounds of some covering array numbers of strength three, degree five and levels v≡2 (mod 4) are improved by applying the method of 3-BD, the upper bounds of some covering array numbers of strength three, degree five and levels v≡2 (mod 4) or g.c.d..{v,18}=3 are also improved by this method.