Construction of Experimental Designs: A Finite Geometric Approach

Abstract

Finite geometries are used in the construction of BIB and PBIB designs with two and more than two-associate classes. Further, finite projective geometries can also be used to construct fractional factorial designs for slevel symmetrical factorial experiments; where s is a prime or a prime power. Under a hierarchical model that includes the general mean, all main effects and a specified set of two-factor interactions, the plans from finite projective geometries have inter-effect orthogonality and are shown to be universally optimal under a hierarchical model within the class of all plans involving the same number of runs. Families of optimal plans from finite projective geometries have been suggested.