OPTIMAL, NONBINARY, VARIANCE-BALANCED DESIGNS

The main result of this paper is a theorem which says that, in some settings, MV-optimal designs cannot have maximum trace of the information matrix. An application of this theorem to proper block designs results in infinite series of MV-optimal non-binary block designs that are MV-superior to all binary block designs of the same parameters; the same ordering is also shown to hold with respect to the Phi(p)-criterion for all sufficiently large p. The issue is one of symmetry of the information matrix versus maximization of its trace, and the implications of balancing these two commonly employed devices are discussed.