ON THE CHARACTERISTIC POLYNOMIALS OF THE INFORMATION MATRICES OF PARTIALLY BALANCED FRACTIONAL 2^m₁+m₂ FACTORIAL DESIGNS OF RESOLUTION VII

Abstract

By utilizing the decomposition of the extended triangular multidimensional partially balanced association algebra, we present an explicit expression for the characteristic polynomial of the information matrix of a partially balanced fractional 2^m₁+m₂ factorial design of resolution VII, which is derived from a partially balanced array. In addition. A-optimal designs with m₁=m₂=3 are presented for 42≤N≤64, where N is the number of observations.