This paper presents a method for designing a robust open spherical microphone array that overcomes the typical problems of open sphere geometries at frequencies related to the zeros of the spherical Bessel functions. The proposed array structure uses only a few additional sampling points inside the spherical volume whose optimal positions are determined by the eigenmodes of the sphere for a given wave number interval. This novel approach minimizes the interpolation error inside the sphere. We illustrate this approach with the design of a 10-th order array using 130 microphones and discuss the simulation results with regard to commonly used error measures (white noise gain, condition number, and interpolation error), and show that the proposed array design compares favorably to previously suggested array designs.