The design of constrained, "plant-friendly" multisine input signals that optimize a geometric discrepancy criterion arising from Weyl's Theorem is examined in this paper. Such signals are meaningful for data-centric estimation and control methods, where uniform coverage of the output state-space contributes greatly to good performance. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in a uniformly distributed output signal that achieves a desirable balance between high and low gain directions, an important consideration when identifying strongly interactive multivariable systems. The solution involves very little user intervention and has significant benefits compared to multisine signals that minimize crest factor. The usefulness of this problem formulation is shown by applying it to a case study involving composition control of a binary distillation column.