Direct detection of a planet around a star by a nulling interferometer, requires to minimize as far as possible the stellar leaks due to the resolved angular size of the star. The original Bracewell configuration features a nulling function in $\theta^{2}$ which is insufficient in many cases. Several interferometric configurations have been proposed in order to improve the quality of the rejection with a nulling function $\theta^{n}$ with $2 \leq n \leq 6$. I proposed recently a method to build linear configurations of telescopes that achieve nulling function $\theta^{n}$ for any even value of n, using the Prouhet-Thué-Morse sequence to select those telescopes where a π phase shift is applied. In a first part, I recall the basis of this method and its generalization to 2D configurations and 1D arrays of non-identical telescopes, or even to configurations where the phase shift is not π. In a next step, I evaluate the efficiency of deep nulling interferometers in real world, i.e. when nulling is not perfect because of variations of distances or of phase shift between telescopes. I conclude that there is a clear advantage given by the highest order systems that keep a better nulling capability than conventional interferometers, even in severe conditions where parameters driving the nulling performance are highly fluctuating.