On Construction of Neighbor Designs

Abstract

Recently a type of block designs called ‘Neighbor designs’ has been developed for serological experiments. It is described as an arrangement of v objects (antigens) on b circular plates (blocks) such that (i) every plate has k objects, not necessarily all distinct, (ii) each object appears r times (not necessarily on r different plates) and (iii) each object is a neighbor of every other exactly λ times. Complete block (i.e, k = v) neighbour design for any odd number of antigens ( v) and incomplete block (i.e., k < v) neighbor designs with λ = 1 and λ > 1 are available in the literature. In this paper, we have suggested a systematic method of constructing complete block neighbor design for any even v. Moreover, we have presented four new methods of construction of incomplete block neighbor designs and have been able to obtain some series of these designs with minimum λ-value through one of the proposed methods.