Two-dimensional balanced sampling plans excluding adjacent units

Hedayat et al. [Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159-170, Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.), Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575-583] first introduced balanced sampling plans for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. While significant advancements have been made in the identification and generalizations of such plans-commonly referred to as BSA sampling plans-little is known concerning the extension of such sampling plans to multi-dimensional populations. This paper will present a review of the pertinent results of one-dimensional BSA sampling plans and a discussion concerning the properties of two-dimensional BSA sampling plans.