In this work, we develop a computational framework for optimal design of experiment in parametric signal reconstruction. We apply this to the optimal design of one dimensional Q-space, Q-ball imaging and multiple Q-shell experimental design. We present how to construct sampling scheme leading to minimal condition number, and compare to state-of-the-art sampling methods. We show in particular a better noise performance of these scheme through Monte-Carlo simulations for the reconstruction of synthetic signal. This demonstrates the impact of this computational framework on acquisition in diffusion MRI.