Top: comparison of 99% detection thresholds obtained with simulations as in Fig. A.1 using different oversampling factors 16 (N_f = 500), 3 (N_f = 90), and 1 (N_f = 30) with the number of tested frequencies N_f given in the legend. The dotted lines are the thresholds obtained from Eq. (A.2), and they agree best with the simulation results without oversampling, while for higher oversampling rates, the required power for a 99% detection is much lower. Bottom: shift in power as a function of detection probability, illustrating that it is not constant. When determining detection probabilities, we correct for oversampling by interpolating these simulations.