Resolvable Dichotomized Split-Set Partially Balanced Incomplete Block Designs

Abstract

A four-associate class association scheme named as Dichotomized Split-Set (DiSS) association scheme is defined for v = 2(p-1)p number of treatments and a method for constructing Partially Balanced Incomplete Block (PBIB) designs based on this association scheme is developed. The proposed designs are cost effective in terms of resources as they require lesser replications. They are resolvable; hence they possess high application potential in areas like multi-site varietal trials where experimenters generally prefer incomplete block designs. The efficiency factors for these designs are computed in comparison to an orthogonal block design and are found to be quite high. For easy generation of these designs for any v = 2p(p - 1); p ≥ 3, an R package called “ResPBIBD” is developed.