A Steiner quadruple system is a Steiner system S(t = 3, k = 4, v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one member of B. Barrau established the uniqueness of S(3, 4, 8), 1 | 2 | 4 | 8 2 | 3 | 5 | 8 3 | 4 | 6 | 8 4 | 5 | 7 | 8 1 | 5 | 6 | 8 2 | 6 | 7 | 8 1 | 3 | 7 | 8 3 | 5 | 6 | 7 1 | 4 | 6 | 7 1 | 2 | 5 | 7 1 | 2 | 3 | 6 2 | 3 | 4 | 7 1 | 3 | 4 | 5 2 | 4 | 5 | 6 and S(3, 4, 10)

Steiner system | Steiner triple system