Families of proper generalized neighbor designs

A generalized neighbor design relaxes the equality condition on the number of times two treatments occur as neighbors in the design. In this article we have constructed a new series of generalized neighbor designs with equal block sizes, a series of neighbor designs of Rees [1967. Some designs of use in serology. Biometrics 23, 779-791] and a series of neighbor designs with two distinct block sizes. Two more new series of GN2 designs are also constructed for even number of treatments. It has been shown that quasi neighbor designs introduced by Preece [1994. Balanced Ouchterlony neighbor designs. J. Combin. Math. Combin. Comput. 15, 197-219] are special cases of generalized neighbor designs with t=2. All the designs given here are binary. A new definition-partially balanced circuit design is introduced which is a special case of generalized neighbor designs with binary blocks.