Various types of environmental assessment are done by taking an array of samples throughout an area. In sampling an area by taking point samples, the choice of sampling locations becomes important. It is assumed here that the task is to take no less than N* samples in a fairly uniform array throughout an area that is a fairly simple shape, such as a rectangle or a combination of a small number of rectangles. Different formulations of the problem are explored. Except in rare instances, a strictly optimum solution would be difficult to compute. "Nearly optimal" solutions to the problem have the minimum or nearly the minimum number of samples required and produce square or nearly square subregions associated with the samples. Approaches for obtaining sampling grids that are nearly optimal are discussed, and one example is presented in detail.

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