Embeddings of Steiner Systems 5(2,4, v)

Publisher Summary This chapter provides an overview of embeddings of Steiner systems S (2,4,ν). A pairwise balanced design (PBD) of index unity, denoted by B[K, ν], is a pair ( X , A ), where X is a ν-set and A is a collection of some subsets (called blocks) of X such that any two distinct elements of X are contained in exactly one block in A and every block in A contains k elements where k ∊ K. A Steiner system S(2,k,v) (also called a (ν,k,l)-BIBD) is a B[k, v ] where one can write B[k, ν] in place of B[{k}, V]. The chapter also reviews a theorem— If u ≥ 85 then any S(2,4,ν) can be embedded in some S(2,4,ν) for every admissible ν≥ 4 u -12.