Construction of two Associate Classes Partially Balanced Incomplete Block Designs With (S-1)2 Replicates

Davinder Kumar Garg; Syed Aadil Farooq

Volume : III, Issue : XII, December - 2014

Construction of two Associate Classes Partially Balanced Incomplete Block Designs With (S-1)2 Replicates

Davinder Kumar Garg, Syed Aadil Farooq

Abstract :

In this paper, we introduce two associate class partially balanced incomplete block (PBIB) designs with (s-1)2 replicates. Each of the s rows and s columns of square array of order s × s are taken as base for Constructing partially balanced incomplete block (PBIB) designs. Also, illustration of construction of some new PBIB designs along with two associate class association schemes have also been given in detail. Summary and Discussion: In this paper, we have established a link between PBIB designs and square array of order s × s in standard order as a result; we get new PBIB designs with two associate classes. Efficiencies of the new designs are also computed for the purpose of comparison. Some designs are new and some newly constructed designs are more efficient, as compared to the existing designs with respective parameters.