The results on optimal designs for diallel crosses are based on
standard linear model assumptions where the general combining ability
effects are taken as fixed. Recently Ghosh and Das (2003) proposed a
random effects model that allows one to first estimate the variance
components and then obtain the variances of these estimates. In this
paper we first propose an unbiased estimate of the ratio of the
variance components which has a one-to-one relation with heritability.
We then obtain a large sample expression of the variance of this
unbiased estimator of the ratio of variance components. Through a
simulation study, it is shown that even for small samples, the large
sample variance is close to the exact variance. Through minimization
of the large sample variance we obtain optimal designs and show
certain connections with the optimization problem under the fixed
effects model.