Analysis of pseudo-random properties of nonlinear congruential generators with power of two modulus by numerical computing of the b-adic diaphony

We consider two nonlinear methods for generating uniform pseudo-random numbers in (0, 1), namely quadratic congruential generator and inversive congruential generator. The combinations of the Van der Corput sequence with the considered nonlinear generators are proposed. We simplify the mixed sequences by a restriction of the b-adic representation of the points. We study numerically the b-adic diaphony of the nets obtained through quadratic congruential generator, inversive congruential generator, their combinations with the Van der Corput sequence, and the simplification of the mixed sequences. The value of the b-adic diaphony decreases with the increase of the number of the points of the simplified sequences which proves that the points of the simplified sequences are pseudo-random numbers. The analysis of the results shows that the combinations of the Van der Corput sequence with these nonlinear generators have good pseudo-random properties as well as the generators.