On the E-optimality of some two-way elimination of heterogeneity designs

In this paper we derive an upper bound for the smallest positive eigenvalues of the C-matrix of a some two-way elimination of heterogeneity designs. This bound is obtained for the class of all designs whose C-matrix admits a representation in the form C = [zeta]1C1 + [zeta]2C2 - [zeta]0C0. On the basis of the above result, a certain E-optimality criterion is given. Furthermore coefficient ed has been introduced which permits us to assess how close the design d is to the optimal design.