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 λ such that each sequence of k distinct elements of [n] is a subsequence of precisely λ 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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- Completely scrambling set of permutations
- Covering array
- Directed t-design
- Sequence covering array
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics