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A combinatorial method for the design of spatially interlaced sparse array antennas is advocated. The cyclic difference sets are used in finding the optimum positions of the elements in the sparse sub-arrays that share a common aperture. A new methodology is proposed for increasing the number of sub-arrays that can be interwoven on a common aperture. Radiation properties of these sparse configuration are investigated by numerical estimations of the antenna array factor at different frequencies.