Minimally replicated PBIB designs for multi-environmental trials

For situations in multi-site varietal trials where the experimenters demand incomplete blocks with unequal sizes, minimum number of replications, or both, new series of incomplete block designs have been presented. The proposed designs are higher associate partially balanced incomplete block designs in two replications having flexible block sizes. These designs are affine resolvable and are optimal in the competing class of resolvable incomplete block designs. The underlying association schemes of these designs are defined. Further, they can be advantageously used for obtaining designs for various stages of breeding trials. An R-package developed for generating these designs has also been demonstrated.