A numerical study was performed on homogeneous field synthesis problem. The influence of geometrical constraints on the important characteristics of uniform field solenoids was studied. These characteristics are: complexity of the shape of current distribution, peak field strength in windings, and relative cost of the solenoid. For superconducting magnets, minimization of the peak field is considered to be one of the primary goals of optimization. An algorithm based on linear programming was proposed to calculate the optimal coil arrangements with minimal peak field. These results were compared to ones obtained by another method, a regularization technique for the field error least squares problem.