Secure pseudorandom bit generators and point sets with low star-discrepancy

The star-discrepancy is a quantitative measure for the irregularity of distribution point set in unit cube that intimately linked to integration error quasi-Monte Carlo algorithms. These popular rules are nowadays also applied very high-dimensional problems. Hence multi-dimensional sets reasonable size with low discrepancy badly needed. A seminal result from Heinrich, Novak, Wasilkowski and Woźniakowski shows existence positive number C such every dimension d there exists an N-element [0,1)d at most Cd∕N. This pure explicit constructions would be desirable. proofs based on random samples which difficult realize practical applications. In this paper we propose use secure pseudorandom bit generators generation order O(d∕N). proposal supported theoretically by means numerical experiments.