  For experiments running in field plots or over time, the observations are
often correlated due to spatial or serial correlation, which leads to
correlated errors in a linear model analyzing the treatment means. Without
knowing the exact correlation matrix of the errors, it is not possible to
compute the generalized least squares estimator for the treatment means and use
it to construct optimal designs for the experiments. In this paper we propose
to use neighbourhoods to model the covariance matrix of the errors, and apply a
modified generalized least squares estimator to construct robust designs for
experiments with blocks. A minimax design criterion is investigated, and a
simulated annealing algorithm is developed to find robust designs. We have
derived several theoretical results, and representative examples are presented.
