  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.
