Uniquely E-optimal designs with n≡2(mod4) correlated observations

In this paper we consider uniquely E-optimal and highly E-efficient designs described by a linear model with design matrices with elements in {−1,0,1}{−1,0,1}. The errors are assumed to be equally positively correlated and to have equal variances. These designs correspond to chemical balance weighing designs or to three-level factorial designs. Designs that satisfy certain conditions are proved to be uniquely E-optimal designs when the number of observations n≡2(mod4). Constructions of such designs are presented, given the existence of an SnSn matrix and a Hadamard matrix. It is also proved that the constructed uniquely E-optimal designs are not in general A- or D-optimal. Finally, the high E-efficiency of the designs of Masaro and Wong (2008) [11] and [12] and certain other designs is shown. These designs can be a good substitute for unknown E-optimal designs in some cases.