  We consider the optimal approximation of certain quantum states of a harmonic
oscillator with the superposition of a finite number of coherent states in
phase space placed either on an ellipse or on a certain lattice. These
scenarios are currently experimentally feasible. The parameters of the ellipse
and the lattice and the coefficients of the constituent coherent states are
optimized numerically, via a genetic algorithm, in order to obtain the best
approximation. It is found that for certain quantum states the obtained
approximation is better than the ones known from the literature thus far.
