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Covering arrays of strength 3 and 4 from holey difference matrices

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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(3, 6, 6p) ≤ 216p 3 + 42p 2 for any prime p > 5; and (3) CAN(4, 6, 2p) ≤ 16p 4 + 5p 3 for any prime p ≡ 1 (mod 4) greater than 5.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Suzhou, 215006, China

    Yang Li, Lijun Ji & Jianxing Yin

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  1. Yang Li
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  2. Lijun Ji
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  3. Jianxing Yin
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Correspondence to Lijun Ji.

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Communicated by C.J. Colbourn.

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Li, Y., Ji, L. & Yin, J. Covering arrays of strength 3 and 4 from holey difference matrices. Des. Codes Cryptogr. 50, 339–350 (2009). https://doi.org/10.1007/s10623-008-9235-1

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  • DOI: https://doi.org/10.1007/s10623-008-9235-1

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