Neighbour balanced block designs for correlated errors

The paper considers a simple block model and assumes that the errors within the blocks are correlated, following a stationary first-order autoregressive process. Gill & Shukla (1985) consider this model, but they restrict the set of the competing designs to a small subset of the possible designs, the binary and equireplicate designs. In the present paper we show that the designs determined by Gill & Shukla are optimal over all possible designs for positive correlations and that neighbour balanced designs in general are highly efficient.