Group Divisible Designs with Two Associate Classes and λ2=1

A pairwise balanced design is an ordered pair S,B , denoted PBD S,B , where S is a finite set of symbols, and B is a collection of subsets of S called blocks, such that each pair of distinct elements of S occurs together in exactly one block of B. Here |S| v is called the order of the PBD. Note that there is no condition on the size of the blocks in B. If all blocks are of the same size k, then we have a Steiner system S v, k . A PBD with index λ can be defined similarly; each pair of distinct elements occurs in λ blocks. If all blocks are same size, say k, then we get a balanced incomplete block design BIBD v, b, r, k, λ . In other words, a BIBD v, b, r, k, λ is a set S of v elements together with a collection of b k-subsets of S, called blocks, where each point occurs in r blocks, and each pair of distinct elements occurs in exactly λ blocks see 1–3 . Note that in a BIBD v, b, r, k, λ , the parameters must satisfy the necessary conditions