Constructions of new orthogonal arrays and covering arrays of strength three

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Ji, Lijun¹  Yin, Jianxing¹ 

[1] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China

关键词: Orthogonal array;    Covering array;    Difference matrix;   

DOI  :  10.1016/j.jcta.2009.06.002

来源: Elsevier

【 摘 要 】

A covering array of size N, strength t, degree k, and order v, or a CA(N t. k. v) in short, is a k x N array on v symbols. In every t x N subarray, each t-tuple column vector occurs at least once. When 'at least' is replaced by 'exactly', this defines an orthogonal array, OA(t, k, v). A difference covering array, or a DCA(k, it: v), over an abelian group G of order v is a k x n array (a(ij)) (1 <= i <= k, 1 <= j <= n) with entries from G, such that, for any two distinct rows I and It of D (1 <= l < h <= k). the difference list Delta(lh) = [d(h1) - d(l1), d(h2) - d(l2),...,d(ln) - d(ln)} contains every element of G at least once. Covering arrays have important applications in statistics and computer Science, as well as in drug screening. In this paper, we present two constructive methods to obtain orthogonal arrays and covering arrays of strength 3 by using DCAs. As a consequence, it is proved that there are an OA(3. 5. v) for any integer v >= 4 and v 0 2 (mod 4), and an OA(3, 6. v) for any positive integer v satisfying gcd(v. 4) 4 2 and gcd(v, 18) 0 3. It is also proved that the size CAN(3. k. v) of a CA(N; 3. k. v) cannot exceed v(3) + v(2) when k = 5 and v 2 (mod 4), or k = 6. v 2 (mod 4) and gcd(v. 18) 4 3. (C) 2009 Elsevier Inc. All rights reserved.

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