Distribution of digital explicit inversive pseudorandom numbers and their binary threshold sequence

Abstract

We study the distribution of s-dimensional points of digital explicit inversive pseudorandom numbers with arbitrary lags. We prove a discrepancy bound and derive results on the pseudorandomness of the binary threshold sequence derived from digital explicit inversive pseudorandom numbers in terms of bounds on the correlation measure of order k and the linear complexity profile. The proofs are based on bounds on exponential sums and earlier relations of Mauduit, Niederreiter and Śarközy between discrepancy and correlation measure of order k and of Brandsẗatter and the third author between correlation measure of order k and linear complexity profile, respectively. © Springer-Verlag Berlin Heidelberg 2009.