Partially balanced t-designs

Abstract

Incomplete block designs bring out useful information from agricultural experimentation with high precision when there is a crunch in resources in terms of homogeneous blocks that can accommodate all the treatments. Balanced incomplete block designs or 2-designs are the most popular class of incomplete block designs. t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t ≥ 2) occur together is a constant. In order to obtain t-balance, we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get balanced t-designs. Two series of such designs are obtained using cyclic development of initial block(s). Association of the proposed designs with t-packing designs are also demonstrated.