@inbook{db2fc5c05f6e4744aa21a08ff0ac0477,

title = "Lattice Rules: How Well Do They Measure Up?",

abstract = "A simple, but often effective, way to approximate an integral over the s-dimensional unit cube is to take the average of the integrand over some set P of N points. Monte Carlo methods choose P randomly and typically obtain an error of 0(N-1/2). Quasi-Monte Carlo methods attempt to decrease the error by choosing P in a deterministic (or quasi-random) way so that the points are more uniformly spread over the integration domain.",

keywords = "Quadrature Rule, Reproduce Kernel Hilbert Space, Star Discrepancy, Quadrature Error, Bernoulli Polynomial",

author = "Hickernell, {Fred J.}",

note = "Funding Information: This research was supported by an HKBU FRG grant 96–97/II-67. Publisher copyright: {\textcopyright} 1998 Springer Science+Business Media New York",

year = "1998",

month = oct,

day = "9",

doi = "10.1007/978-1-4612-1702-2_3",

language = "English",

isbn = "9780387985541",

series = "Lecture Notes in Statistics",

publisher = "Springer",

pages = "109–166",

editor = "Peter Hellekalek and Gerhard Larcher",

booktitle = "Random and Quasi-Random Point Sets",

edition = "1st",

}