Construction of Two Factor Asymmetrical Factorial Designs that are Characterized by Balance with Orthogonal Factorial Structure (BAFDs)

Abstract

The construction of two factor BAFD's with block size equal to the levels levels of the first factor or block size equal the levels of the second factor has been pointed out. It should be noted that the construction methods involved utilizes balanced arrays, orthogonal arrays and transitive arrays. Several theorems that enable generation of resolvable balanced incomplete block designs have been proved. These theorems involve galois fields and methods of step cycles. Using resolvable balanced incomplete block designs and balanced arrays we have also pointed out the construction of two factor BAFD's with block size which is equal to a common multiple of the levels of the two factors. It should also be noted that the designs constructed are such that the main effects of each of the two factors are estimated with full/maximum efficiency. The designs are balanced with orthogonal factorial structure (OFS).