Growth of the perfect sequence covering array number

Abstract In this note we answer positively an open question posed by Yuster in 2020 [14] on the polynomial boundedness of perfect sequence covering array number $$g(n,k)$$ g ( n , k ) (PSCA number). The latter determines (renormalized) minimum row-count that arrays (PSCAs) can possess. PSCAs are matrices with permutations $$S_n$$ S as rows, such each ordered k -sequence distinct elements $$[n]$$ [ ] is covered same rows. We obtain result after illuminating isomorphism between structure from design theory and a special case min-wise independent permutations. Afterwards, point out asymptotic bounds constructions be transferred these two structures. Moreover, sharpen lower for g ( n , ) improve upper 4) 3), some concrete values . conclude questions propose new matrix class being potentially advantageous searching PSCAs.