Abstract
The notion of a detecting array (DTA) was proposed, recently, by Colbourn and McClary in their research on software interaction tests. Roughly speaking, testing with a (d, t)−DTA(N, k, v) can locate d interaction faults and detect whether there are more than d interaction faults. In this paper, we establish a general lower bound on sizes of DTAs and explore an equivalence between optimal DTAs and super-simple orthogonal arrays (OAs). Taking advantage of this equivalence, a great number of DTAs are constructed, which are all optimal in the sense of their sizes. In particular, an optimal (2, t)−DTA(N, 5, v) of strength t = 2 or 3 is shown to exist whenever v ≥ 3 excepting \({(t, v) \in \{(2, 3), (2, 6),(3, 4), (3, 6)\}}\) .
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Communicated by C. J. Colbourn
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Shi, C., Tang, Y. & Yin, J. The equivalence between optimal detecting arrays and super-simple OAs. Des. Codes Cryptogr. 62, 131–142 (2012). https://doi.org/10.1007/s10623-011-9498-9
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DOI: https://doi.org/10.1007/s10623-011-9498-9