Upper estimates for the element number of non-redundant antenna configurations on square and hexagonal grids

Estimates for the maximum number of elements of non-redundant configurations on integer square and hexagonal grids of given sizes are derived (a “non-redundant” configuration implies that the vector differences between its elements are all distinct). When projecting a large 2-D interferometer or a telescope, such an estimate can be used as a guide for evaluating the maximum possible number of antennas in a non-redundant configuration that can be arranged within a given area. The suggested estimates are empirical and based on the available data. They are obtained by reducing the problem to the linear case and by generalizing the method applied therein. Examples of applying the method are presented.