On the Selection of Optimal Balanced Incomplete Block Design using Different Types of Designs.

Abstract:

The choice of selecting the best among the types of balanced incomplete block designs (BIBDs) have brought about some controversies in combinatorial design. Prominent methods of constructing BIBD have been proposed by different authors, but none has been juxtaposed the designs with respect to type. In this paper, we proposed the adoption of the concept of optimality criteria such as: A-, D-, E- , and T – optimality criterion to select the best design based on their optimality values using a (15, 15, 7, 7, 3) simulated balanced incomplete block design. A dual design, residue design and derived design were selected as the major three types of BIBDs for investigation. The findings revealed that dual design is the best balanced incomplete block design based on its high optimal value. We discovered that residue and derived design obtained from the simulated balanced incomplete block design by method of block selection and intersection becomes a standard balanced incomplete block design.