Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
In this paper, we give explicit constructions of point sets in the s-dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high-dimensional periodic functions. In the classical measure $P_{\alpha}$ of the worst-case error introduced by Korobov, the convergence, …