Development of some useful generators to obtain partially neighbor balanced designs

Some Pairwise Balanced Designs

A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...

An Algorithm to Generate Neighbor Balanced Binary Block Designs

Ahmed and Akhtar (2007) developed some algorithms to generate neighbor balanced designs. Here, a new algorithm is developed to generate circular neighbor balanced binary block designs for v = 2k in 2(v-1) blocks when blocks are well separated. A catalogue of circular neighbor balanced binary block designs for v up to 50 is presented.

Review of One Dimensional Neighbor Balanced Designs Since 1967

Rees (1967) introduced neighbor designs in serology. Since then it is well investigated field. Neighbor balanced designs are more useful to remove the neighbor effects in experiments where the performance of a treatment is affected by the treatments applied to its neighboring plots. Neighbor designs ensure that treatment comparisons will be less affected by neighbor effects as possible. This pa...

Optimality of neighbor-balanced designs for total effects

The purpose of this paper is to study optimality of circular neighborbalanced block designs when neighbor effects are present in the model. In the literature many optimality results are established for direct effects and neighbor effects separately, but few for total effects, that is, the sum of direct effect of treatment and relevant neighbor effects. We show that circular neighbor-balanced de...

A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties