In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the total number of binary variables. We will illustrate the validity of our proposed method by solving a difficult known instance (N=126) of the D-optimal design.