Reducing system complexity and cost in synthesizing a sparse array antenna design is a challenging task for practical communication systems, such as radar systems and space communication. In this paper, a hybrid technique to synthesize a linear sparse array antenna design is described. This technique is developed using two methods. The first method is a combinatorial approach that applies cyclic difference sets (CDS) integers to significantly reduce the number of antenna elements. The approach and procedure used to apply the new CDS method to configure a linear sparse array, with significant reduction of the spatial antenna dimension, is described. The second method, applied to the array result of the first method, is amplitude tapering using a binomial array approach to reduce the sidelobes level (SLL). The simulation and measurement results of the sample sparse array design showed that the SLL was reduced in comparison to the sparse array design using only the combinatorial CDS method.