A PSCA$$(v, t, \lambda )$$ ( v , t , λ ) is a multiset of permutations of the v-element alphabet $$\{0, \dots , v-1\}$$ { 0 , ⋯ , v - 1 } , such that every sequence of t distinct elements of the alphabet appears in the specified order in exactly $$\lambda $$ λ of the permutations. For $$v \geqslant t \geqslant 2$$ v ⩾ t ⩾ 2 , we define g(v, t) to be the smallest positive integer $$\lambda $$ λ , such that a PSCA$$(v, t, \lambda )$$ ( v , t , λ ) exists. We show that $$g(6, 3) = g(7, 3) = g(7, 4) = 2$$ g ( 6 , 3 ) = g ( 7 , 3 ) = g ( 7 , 4 ) = 2 and $$g(8, 3) = 3$$ 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 $$v \leqslant 32$$ v ⩽ 32 and $$3\leqslant t\leqslant 6$$ 3 ⩽ t ⩽ 6 . We also prove a number of restrictions on the distribution of symbols among the columns of a PSCA.