Optimal partial diallel crosses

Even in the absence of blocks, each cross in a partial diallel cross design can be formally identified with a 'block' of size two and thus the design itself can be identified with a binary block design. We show that unblocked partial diallel crosses, so linked with a certain class of group divisible designs, are uniquely E-optimal in general and also uniquely D-and A-optimal in the saturated case. Further results on E-optimality, applicable even when the number of parental lines does not admit a factorisation, are also derived. The issue of optimal or efficient blocking of partial diallel crosses is discussed.