On Perfect Sequence Covering Arrays
A PSCA(v, t, λ) is a multiset of permutations of the
v-element alphabet {0, ..., v-1} such that every sequence of
t distinct elements of the alphabet appears in the specified order
in exactly λ of the permutations. For v ≥ t ≥ 2, we
define g(v, t) to be the smallest positive integer λ such
that a PSCA(v, t, λ) exists. We show that g(6, 3) = g(7, 3)
= g(7, 4) = 2 and g(8, 3) = 3. Using suitable permutation
representations of groups we make improvements to the upper bounds
on g(v, t) for many values of v ≤ 32 and 3≤ t≤ 6. We
also prove a number of restrictions on the distribution of symbols
among the columns of a PSCA.