Some D-optimal odd-equireplicated designs for a covariate model

Abstract

A linear model with one treatment at V levels and the first order regression on K continuous covariates with values on the K-cube is considered. The main interest is restricted to the subclass of odd-equireplicated designs, i.e. designs with equal number R ≡ 1 mod 2 of observations per treatment level. Lopes Troya (1982) has constructed families of designs d which attain the upper bound of the determinant of the information matrix M( d). In this paper another series of D-optimal designs is constructed for which M( d) has different structure from the known ones, in the cases where V R is an integer. Also, for N = VR ≡ i mod 4 observations and V > iR, new D-optimal designs are constructed for which the maximum number of covariates is V − iR, where i = 1, 2.