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generally larger, so it will have less discriminating power for the more impor-
tant low-dimensional projections. In practice, the weights are often taken all
equal to 1.
Specific instances of these criteria, and search results for good parameters
for specific types of digital nets, are reported in [64,21,65,63]. A special case of
the first of these four criteria has been widely used to assess the uniformity of
F
2
-linear RNGs [45,66,31,67,10,42].
7Conluon
Low-discrepancy point sets and sequences used for QMC, and the point sets
formed by vectors of successive output values produced by RNGs, have much
in common. They are often defined via similar linear recurrences. We also want
both of them to be highly uniform in the unit hypercube. However, the figures of
merit commonly used to measure their uniformity are slightly different. One of
the reasons for this difference is the difference of cardinality between those types
of point sets: For RNGs, the cardinality is huge and we must restrict ourselves
to criteria that can be computed without enumerating the points explicitly, for
example. For QMC, on the other hand, certain discrepancies are motivated by
the fact that they provide explicit error bounds or variance bounds on certain
classes of functions.
References
1. Knuth, D.E.: The Art of Computer Programming, 3rd edn. Seminumerical Algo-
rithms, vol. 2. Addison-Wesley, Reading (1998)
2. L'Ecuyer, P.: Uniform random number generation. Annals of Operations Re-
search 53, 77-120 (1994)
3. L'Ecuyer, P.: Uniform random number generation. In: Henderson, S.G., Nelson,
B.L. (eds.) Simulation. Handbooks in Operations Research and Management Sci-
ence, ch.3, pp. 55-81. Elsevier, Amsterdam (2006)
4. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods.
SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63.
SIAM, Philadelphia (1992)
5. Law, A.M., Kelton, W.D.: Simulation Modeling and Analysis, 3rd edn. McGraw-
Hill, New York (2000)
6. L'Ecuyer, P., Buist, E.: Simulation in Java with SSJ. In: Kuhl, M.E., Steiger, N.M.,
Armstrong, F.B., Joines, J.A. (eds.) Proceedings of the 2005 Winter Simulation
Conference, pp. 611-620. IEEE Press, Pistacaway (2005)
7. L'Ecuyer, P.: Pseudorandom number generators. In: Platen, E., Jaeckel, P. (eds.)
imulation Methods in Financial Engineering. Encyclopedia of Quantitative Fi-
nance, Wiley, Chichester (forthcoming, 2008)
8. Deng, L.Y.: Ecient and portable multiple recursive generators of large order.
ACM Transactions on Modeling and Computer Simulation 15(1), 1-13 (2005)
9. L'Ecuyer, P., Simard, R.: TestU01: A C library for empirical testing of random
number generators. ACM Transactions on Mathematical Software, Article 22 33(4)
(2007)
