Some optimal designs for sampling in two dimensions

Employing a superpopulation model, we derive conditions for which a sampling design of a two–dimensional finite population is optimal in the sense of minimum average variance, when the estimator of the population mean is the sample mean. We find that an overall optimal design does not exist, but that, if we consider three subclasses of two–dimensional sampling designs, then the optimal design within each subclass is a type of systematic sampling.