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New covering array numbers
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DOI：10.1016/j.amc.2019.01.069.png)
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Abstract
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A covering array CA (N; t, k, v) is an N x k array on v symbols such that each N x t subarray contains as a row each t-tuple over the v symbols at least once. The minimum N for which a CA (N; t, k, v) exists is called the covering array number of t, k, and v, and it is denoted by CAN (t, k, v). We prove that CA (N; t + 1, k + 1, v) can be obtained from the juxtaposition of v covering arrays CA (N-0; t, k, v), ..., CA (Nv-1; t, k, v), where N = Sigma(v-1)(i=0) N-i. Given this, we developed an algorithm that constructs all possible juxtapositions and determines the nonexistence of certain covering arrays which allow us to establish the new covering array numbers CAN (4, 13, 2) = 32, CAN (5, 8, 2) = 52, CAN (5, 9, 2) = 54, CAN (5, 14, 2) = 64, CAN(6, 15, 2) = 128, and CAN (7, 16, 2) = 256. Additionally, the computational results are the improvement of the lower bounds of 13 covering array numbers. (C) 2019 Elsevier Inc. All rights reserved.
Keywords:
Covering array number
Juxtaposition of covering arrays
Non-isomorphic covering arrays
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