  New crop varieties are extensively tested in multi-environment trials in
order to obtain a solid empirical basis for recommendations to farmers. When
the target population of environments is large and heterogeneous, a division
into sub-regions is often advantageous. When designing such trials, the
question arises how to allocate trials to the different subregions. We consider
a solution to this problem assuming a linear mixed model. We propose an
analytical approach for computation of optimal designs for best linear unbiased
prediction of genotype effects and pairwise linear contrasts and illustrate the
obtained results by a real data example from Indian nation-wide maize variety
trials. It is shown that, except in simple cases such as a compound symmetry
model, the optimal allocation depends on the variance-covariance structure for
genotypic effects nested within sub-regions.
