A2-optimal designs: the nearly-balanced case

Abstract

Due to cost constraints, there are often times when balanced designs are not feasible. Unbalanced designs are also used in cases where some treatment combinations may be of particular interest, so the experimenter chooses to sample more heavily from them. A new lower bound for the A2 -optimality measure that can be applied to both balanced and nearly-balanced experimental designs is provided. This bound is proved to be tight and achievable. New methods for constructing infinite families of saturated and supersaturated nearly-balanced A2-optimal designs are also provided.