Optimal designs for nearest-neighbor analysis

For field trials of v varieties in blocks of size k, in the presence of a random trend, data may be analyzed by the nearest-neighbor method based on first differences. The variance components model for this analysis is the linear variance (LV) model. Optimal designs for the case k less than or equal to v were given by Martin et al. (J. Statist Plann. Inference 34 (1993) 433-450) and the case v < k less than or equal to 2v by Martin (1998). In this paper, for the general case of any k and v we show that a universally optimal design can be constructed from a semibalanced array if the varieties within blocks are arranged in a particular order. The order does not depend on the magnitudes of the variance components. (C) 2000 Elsevier Science B.V. All rights reserved.