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In this letter, the antenna array design problem in minimum redundancy (MR) multiple-input-multiple-output (MIMO) radars is addressed, which seeks to maximize the virtual array aperture for a given number of transmitting and receiving (Tx/Rx) elements. Based on difference bases and cyclic difference sets (CDSs), a combinatorial method is proposed for the optimal design of Tx/Rx antenna arrays. The theoretical limits of the redundancy of MIMO virtual arrays constructed by the method for both one-dimensional and two-dimensional cases are derived. Numerical results are also presented, showing notable improvement in the spatial resolution of MIMO radar system over those reported in the literature.