论文信息 - A lower bound for rank 2 lattice rules

A lower bound for rank 2 lattice rules

We give a lower bound for a quality measure of rank 2 lattice rules which shows that an existence result of Niederreiter is essentially best possible.

Friedrich Pillichshammer

[1] Gerhard Larcher. A best lower bound for good lattice points , 1987 .

[2] Lauwerens Kuipers,et al. Uniform distribution of sequences , 1974 .

[3] Lattice rules: projection regularity and unique representations , 1990 .

[4] Harald Niederreiter,et al. Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[5] H. Niederreiter. Existence of good lattice points in the sense of Hlawka , 1978 .

[6] Harald Niederreiter,et al. Lattice rules for multiple integration and discrepancy , 1990 .

[7] I. Sloan. Lattice Methods for Multiple Integration , 1994 .

[8] E. Hlawka. Zur angenäherten Berechnung mehrfacher Integrale , 1962 .

[9] Harald Niederreiter. The existence of efficient lattice rules for multidimensional numerical integration , 1992 .