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The minimum number of permutations such a sequence covering array can have is $t!$ and Levenshtein conjectured that if a sequence covering array with $t!$ permutations exists, then $v \\in \\{t,t+1\\}$. In this paper, we prove that if an \\textsf{SCA}$(7!;7,v)$ exists, then $v \\leq 9$. 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Gentle, Daniel Horsley, Ian M. Wanless","submitted_at":"2024-11-26T06:28:11Z","abstract_excerpt":"A sequence covering array, denoted \\textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\\{0, \\dots, v-1 \\}$ such that each sequence of $t$ distinct elements of $\\{0, \\dots, v-1\\}$ reads left to right in at least one permutation. The minimum number of permutations such a sequence covering array can have is $t!$ and Levenshtein conjectured that if a sequence covering array with $t!$ permutations exists, then $v \\in \\{t,t+1\\}$. In this paper, we prove that if an \\textsf{SCA}$(7!;7,v)$ exists, then $v \\leq 9$. 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