Abstract
An (n, k) sequence covering array is a set of permutations of [n] such that each sequence of k distinct elements of [n] is a subsequence of at least one of the permutations. An (n, k) sequence covering array is perfect if there is a positive integer \(\lambda \) such that each sequence of k distinct elements of [n] is a subsequence of precisely \(\lambda \) of the permutations. While relatively close upper and lower bounds for the minimum size of a sequence covering array are known, this is not the case for perfect sequence covering arrays. Here we present new nontrivial bounds for the latter. In particular, for \(k=3\) we obtain a linear lower bound and an almost linear upper bound.
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Notes
Unless stated otherwise, all logarithms are in base 2.
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Communicated by C. J. Colbourn.
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Yuster, R. Perfect sequence covering arrays. Des. Codes Cryptogr. 88, 585–593 (2020). https://doi.org/10.1007/s10623-019-00698-7
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DOI: https://doi.org/10.1007/s10623-019-00698-7