INCOMPLETE BLOCK-DESIGNS WITH SPATIAL LAYOUTS WHEN OBSERVATIONS ARE DEPENDENT

A recent paper (Martin and Eccleston, J. Statist. Plann. Inference 28, 1991) considers block designs when the plots within a block are linearly arranged, and observations within a block are dependent. Designs were discussed that are optimal either within a restricted class of designs for all dependence structures or for all designs over a restricted class of dependence structures. Some cases in which non-binary designs are optimal were also considered. In this paper we generalize those results to the case that the plots within a block are spatially arranged. and introduce new designs that may be appropriate when the dependence structure has additional symmetries.