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A regular method for synthesizing a planar aperiodic thinned array antenna (AA) with a low peak sidelobe level is suggested. It is based on using specific combinatorial constructions - noncyclic difference sets (DSs). The method uses the fact that when the elements of an equiamplitude AA are arranged according to a DS law, its power pattern takes constant value in the net of uniformly located space points in the sidelobe region, and this value is less than , where is the element number. In distinction to the method using cyclic DSs (see Leeper, 1999) which enables one to build planar AAs only on rectangular grids with co-prime sidelengths, the represented method omits such a constraint. The most important class of the noncyclic 2-D DSs is represented by the sets of Hadamard type (sets). Based on such sets, rectangular and square aperiodic roughly half-filled AAs can be built. Here, the numerical results obtained for the square AAs, with the element number in the array up to 300, are presented.