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The positioning of nulls in an antenna array field pattern is essential to the performance of the antenna, in being capable of blocking interference. The null placement must be achieved in such a way that the field pattern in other directions is not adversely affected. One of the most efficient methods of null placement is by perturbing only the phases of the array elements. This document presents two approaches to the placement of nulls by phase perturbation. The first is a least squares method based on exact of approximate null placement, applicable to one-dimensional arrays and extendable to two-dimensional arrays, developed for real quiescent patterns which apparently allows polygonal arrays (in this study, octagonal arrays) to be considered. The second is a minimax method in one or two dimensions based on null placement, which readily permits the omission of failed elements and which involves only the perturbation of selected element phases or amplitudes. Keywords: Great Britain, Ladar antennas.