Let t, v, k, λ be positive integers satisfying v > k > t. A t-(v, k, λ) design is an ordered pair (V,B), where V is a finite set of v points, B is a collection of k-subsets of V , say blocks, such that every t-subset of V occurs in exactly λ blocks in B. In what follows we simply write t-designs. A 3-(v, 4, 1) design is called a Steiner quadruple system and denoted by SQS(v). It is known that a...