**COT 5715: Random Number
Generation
General Bibliography & Papers for Students to Present in
Class**

- J. H. Ahrens and U. Dieter,
*Non-Uniform Random Numbers*, Institut für Mathematische Statistik, Technische Hochschule, Graz, Austria, 1974. - N. S. Altman, "Bit-wise
behavior
of random number generators,"
*SIAM J. Sci. Stat. Comput.*,**9**: 941-949,1988. - S. L. Anderson, "Random
number
generators on vector supercomputers and other advanced
architectures,"
*SIAM Review*,**32**: 221-251, 1990. - S. Aluru and G. M. Prabhu and J. Gustafson, "A
random number generator for parallel computers,"
*Parallel Computing*,**18**: 839-847, 1992. - D. L. Andrè and G. L.
Mullen and H. Niederreiter, "Figures
of
merit for digital multistep pseudorandom number generators,"
*Mathematics of Computation*,**54**: 737-748, 1990. - A. C. Arvillas and D. G. Maritsas, "Partitioning
the
period of a class of
*m*-sequences and applications to pseudorandom number generation,"*J. of the ACM*,**25**: 675-686, 1978. - B. C. Bromley, "Quasirandom number generator for parallel Monte Carlo algorithms," Journal of Parallel and Distributed Computing, 38: 101-104, 1996.
- W. A. Beyer and R. B. Roof and D. Williamson, "The
lattice
structure of multiplicative pseudo-random vectors,"
*Mathematics of Computation*,**25**: 345-363, 1971. - G. E. P. Box and M. E. Miller, "A
note on the generation of normal random deviates,"
*Ann. Math. Stat.*,**29**: 610-611, 1958 - E. Braaten and G. Weller, "An
Improved
Low-Discrepancy Sequence for Multidimensional Quasi-Monte
Carlo Integration,"
*Journal of Computational Physics*,**33**: 249-258, 1979. - P. Bratley and B. L. Fox, "Algorithm
659:
Implementing Sobol's quasirandom sequence generator,"
*ACM transactions on Mathematical Software*,**14(1)**: 88-100, 1988. - P. Bratley and B. L. Fox and H. Niederreiter, "Implementation
and
tests of low-discrepancy sequences,"
*ACM Transactions on Modeling and Computer Simulation*,**2**: 195-213, 1992. - R. P. Brent, "Uniform Random Number Generators for Supercomputers," in "Proceedings of the Fifth Australian Supercomputer Conference", pp. 95-104, 1992.
- R. P. Brent, "On
the
periods of generalized Fibonacci recurrences,"
*Mathematics of Computation*,**63**: 389-401, 1994. - B.C. Bromley, "Quasirandom
number
generators for parallel Monte Carlo algorithms,"
*Journal of Parallel and Distributed Computing*,**38**: 101-104, 1996. - R.E. Caflisch, "Monte
Carlo
and quasi-Monte Carlo methods,"
*Acta Numerica*,**7**: 1-49, 1998. - H. Chaix and H. Faure, "Discrepance
et
diaphonie en dimension un,"
*Acta Arithmetica,***63**: 103-141, 1993. - P. Coddington, "Analysis of random number generators using
Monte Carlo simulation,"
*Int. J. of Mod. Phys. C*,**5**: 547-560, 1994. - P. Coddington, "Tests of random number generators using Ising
model simulations,"
*Int. J. of Mod. Phys. C*,**7**: 295-303, 1996 - B. J. Collings and G. B. Hembree, "Initializing
generalized
feedback shift register pseudorandom number generators,"
*J. of the ACM*,**33:**706-711, 1986. - R. R. Coveyou, "Random number generation is too important to
be left to chance,"
*Studies in Applied Math.*,**3**: 70-111, 1969. - R. R. Coveyou and R. D. MacPherson, "Fourier
analysis
of uniform random number generators,"
*J. of the ACM*,**14**: 100-119, 1967. - R. Couture and P. L'Ecuyer, "On
the
lattice structure of certain linear congruential sequences
related to AWC/SWB generators," Math. Comput.,
**62**: 799-808, 1994. - R. Couture and P. L'Ecuyer, "Distributed
properties
of multiply-with-carry random number generators,"
*Math. Comput.*,**66**: 591-607, 1997. - S. A. Cuccaro and M. Mascagni and D. V. Pryor, "Techniques for testing the quality of parallel pseudorandom number generators," in "Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing", SIAM: Philadelphia, Pennsylvania, pp. 279-284, 1995.
- I. Deák, "Uniform
random
number generators for parallel computers,"
*Parallel Computing*,**15**: 155-164, 1990. - L. Y. Deng and K. H. Chan and Y. Yuan, "Random number generators for multiprocessor
systems,"
*Int. J. Model. Simul.*.**14**: 185-191, 1994. - L. Y. Deng and H. Xu, "A
system of high-dimensional, efficient, long-cycle and portable
uniform random number generators,"
*ACM Transactions on Modeling and Computer Simulation*,**13 (4)**: 299-309, 2003. - M. Deleglise and J. Rivat, "Computing
π(x): the Meissel, Lehmer,
Lagarias, Miller, Odlyzko method,"
*Math. Comput.*,**65**: 235-245, 1996. - A. De'Matteis and S. Pagnutti, "Parallelization of random number generators
and long-range correlations,"
*Numer. Math.*,**53**: 595-608, 1988. - A. De'Matteis and S. Pagnutti, "A class of parallel random number generators,"
*Parallel Computing*,**13**: 193-198, 1990. - A. De'Matteis and S. Pagnutti, "Long-range correlations in linear and
non-linear random number generators,"
*Parallel Computing*,**14**: 207-210, 1990. - A. De'Matteis and S. Pagnutti, "Controlling
correlations
in parallel Monte Carlo",
*Parallel Computing*,**21**: 73-84, 1995. - E. De Doncker and R. Zanny and M. Ciobanu and Y. Guan, Distributed
quasi
Monte-Carlo methods in a heterogeneous environment," in
*Proceedings of the Heterogeneous Computing Workshop 2000*, pp. 200-206, 2000. - L. Devroye,
*Non-uniform Random Variate Generation*, Springer-Verlag: New York, 1986. - M. J. Durst, "Testing parallel random number generators,"
in
*Computing Science and Statistics: Proceedings of the XXth Symposium on the Interface*, pp. 228-231, 1988. - M. J. Durst, "Using
linear
congruential
generators for parallel random number generation," in
*Proceedings of the 1989 Winter Simulation Conference: Society for Computer Simulation*,, E. A. MacNair and K. J. Musselman and P. Heidelberger, eds., IEEE Press, pp. 462-466, 1989. - W. F. Eddy, "Random number generators for parallel
processors,"
*J. Comput. Appl. Math.*,**31**: 63-71, 1990. - J. Eichenauer-Herrmann, "Inversive
congruential
pseudorandom numbers avoid the planes,"
*Math. Comput.*,**56**: 297-301, 1991. - J. Eichenauer-Herrmann and E. Herrmann and S. Wegenkittl, "A
survey of quadratic and inversive congruential pseudorandom
numbers,"
*Lecture Notes in Statistics*,**127**: 66-97, 1998. - J. Eichenauer and H. Groethe and J. Lehn and A. Topuzŏglu, "A multiple recursive non-linear congruential
pseudorandom number generator,"
*Manuscripta Math*.,**58**: 315-326, 1987. - J. Eichenauer and H. Groethe and J. Lehn, "Marsaglia's lattice test and non-linear
congruential pseudorandom number generators,"
*Metrika*,**35**: 241-250, 1988. - J. Eichenauer and J. Lehn, "A
nonlinear congruential pseudorandom number generator,"
*Statist. Hefte*,**37**: 315-326, 1986. - J. Eichenauer and J. Lehn and A. Topuzŏglu, "A
nonlinear congruential pseudorandom number generator with
power of two modulus,"
*Math. Comput.*,**51**: 757-759, 1988. - J. Eichenauer-Herrmann and H. Groethe and H. Niederreiter and
A. Topuzŏglu, "On the lattice structure of non-linear
generators with modulus 2
^{α},"*J. Comput. Appl. Math.*,**31**: 81-85, 1990. - J. Eichenauer-Herrmann, and H. Niederreiter, "Digital
inversive
pseudorandom numbers,"
*ACM Transactions on Modeling and Computer Simulation*,**4**: 339-349, 1994. - J. Eichenauer-Herrmann, "Pseudorandom
generation
by nonlinear methods,"
*International Statistical Review*,**63**: 247-255, 1995. - K. Entacher, "Bad
subsequences
of well-known linear congruential pseudorandom number
generators,"
*ACM Trans. Model. Comput. Simul.*,**8**: 61-70, 1998. - K. Entacher, "Parallel
streams
of linear random numbes in the spectral test,"
*ACM Trans. Model. Comput. Simul.*, 9: 31-44, 1999. - H. Faure, "Using permutations to reduce discrepancy,"
*J. Comp. Appl. Math.*,**31**: 97-103, 1990. - H. Faure, "Good Permutations for Extreme Discrepancy",
*Journal of Number Theory*,**42**: 47-56, 1992. - H. Faure, "Discrépance de suites associées à un système de numération (en dimension s),"
*Acta Arith.*,**41(4)**: 337-351, 1982, in French. - H. Faure and S. Tezuka, "A
New Generation of Digital (0,s)-Sequences,"
in
*Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, 2000*, H. Niederreiter, et al., eds., Springer, 2001. - A. M. Ferrenberg and D. P. Landau and Y. J. Wong, "Monte
Carlo
simulations: Hidden errors from `good' random number
generators,"
*Phys. Rev. Let.*,**69**: 3382-3384, 1992. - G. S. Fishman, "Multiplicative
congruential
random number generators with modulus 2
^{β}: an exhaustive analysis for β = 32 and a partial analysis for β = 48,"*Math. Comput.*,**54**: 331-344, 1990. - G. S. Fishman and L. S. Moore III, "An
exhaustive
analysis
of multiplicative congruential random number generators with
modulus 2
^{31}-1,"*SIAM J. Sci. Stat. Comput.,***1**: 24-45, 1986. - P. Frederickson and R. Hiromoto and T. L. Jordan and B. Smith
and T. Warnock, "Pseudo-random trees in Monte Carlo",
*Parallel Computing*,**1**: 175-180, 1984. - P. Frederickson and R. Hiromoto and J. Larson, "A parallel Monte Carlo transport algorithm
using a pseudo-random tree to guarantee reproducibility,"
*Parallel Computing*,**4**: 281-290, 1987. - B. L. Fox, "Algorithm
647:
Implementation
and Relative Efficiency of Quasirandom Sequence Generators,"
*ACM Transactions on Mathematical Software (TOMS)*,**12(4)**: 362-376, 1986 - M. Fushimi, "Increasing the orders of equidistribution of the
leading bits of the Tausworthe sequence,"
*Inform. Proc. Lett.*,**16**: 189-192, 1983. - M. Fushimi, "An equivalence relation between Tausworthe and
GFSR sequences and applications,"
*Applied Math. Lett.*,**2**: 135-137, 1989. - M. Fushimi, "Random
number
generation on parallel processors," in
*Proceedings of the 1989 Winter Simulation Conference: Society for Computer Simulation*, E. A. MacNair and K. J. Musselman and P. Heidelberger, eds., IEEE Press, pp. 459-461, 1989. - M. Fushimi and S. Tezuka, "The
*k*-distribution of generalized feedback shift register pseudorandom numbers,"*Comm. of the ACM*,**26**: 516-523, 1983. - S. W. Golomb,
*Shift Register Sequences*, Revised Edition, Aegean Park Press: Laguna Hills, California, 1982. - E. R. Golder and J. G. Settle, "The
Box-Muller
method
for generating pseudo-random normal deviates,"
*Appl. Statist.*,**25**: 12-20, 1972. - P. Grassberger, "On correlations in 'good' random number
generators,"
*Phys. Lett. A*,**181**: 43-46, 1993. - H. Grothe, "Matrix generators for pseudo-random vector
generation,"
*Statist. Hefte.*,**28**: 233-238, 1987. - M. Goresky and A. Klapper, " Efficient
multiply-with-carry
random number generators with maximal period,,"
*ACM Transactions on Modeling and Computer Simulation*,**13**: 310-321, 2003. - J. H. Halton, "Pseudo-random
trees:
multiple
independent sequence generators for parallel and branching
computations,"
*J. Comput. Phys.*,**84**: 1-56, 1989. - J. H. Halton, "Algorithm
247:
Radical-inverse quasi-random point sequence,"
*Communications of the ACM*,**7(12)**: 701-702, 1964. - J. H. Halton, "On
the
efficiency of certain quasi-random sequences of points in
evaluating multi-dimensional integrals,"
*Numer. Math.*,**2**: 84-90, 1960. - J. H. Halton, "Sequential
Monte
Carlo,"
*Proceedings of the Cambridge Philosophical Society*,**58**: 57-78, 1962. - J. H. Halton, "Sequential Monte Carlo Techniques for the
Solution of Linear Systems",
*Journal of Scientific Computing*, 9: 213-257, 1994. - J. M. Hammersley and D. C. Handscomb,
*Monte Carlo Methods*, Chapman and Hall: London, 1964. - S. Heinrich, "Efficient
algorithms
for computing the L
_{2}-discrepancy,"*Math. Comput.*,**65(216)**: 1621-1633, 1996. - P Hellekalek and H. Niederreiter, "The
weighted
spectral test: Diaphony,"
*ACM Trans. Model. Comput. Simul.*, 8: 43-60, 1998. - G. W. Hill, "Cyclic
properties
of pseudo-random sequences of Mersenne prime residues,"
*Comput. J.*,**22**: 80–85, 1979. - E. Hlwaka, "Funktionen von beschränkter Variation in der Theorie der
Gleichverteiling,"
*Ann. Mat. Pura Appl.*,**54**: 325-333, 1961. - T. E. Hull and A. R. Dobell, "Random Number Generators," SIAM Review, 4(3): 230-254,
1962.

- B. L. Holian and O. E. Percus and T. T. Warnock and P. A.
Whitlock, "Pseudorandom
number
generators for massively parallel molecular-dynamics
simulations,"
*Phys. Rev. E*,**50(2, pt. B)**: 1607-1615, 1994. - K. Kankaala and T. Ala-Nissila and I. Vattulainen, "Bit level correlations in some pseudorandom number generators," Research Institute for Theoretical Physics, University of Helsinki, Preprint series in theoretical physics: HU-TFT-93-41, 1993.
- S. Kirkpatrick and E. P. Stoll, "A
very fast shift-register sequence random number generator
turbulence simulation,"
*J. Comput. Phys.*,**40**: 517-526, 1981. - L. Kocis and W.J. Whiten, "Computational
investigations
of low-discrepancy sequences,"
*ACM transactions on Mathematical Software*,**23(2)**: 266-294, 1997. - A. E. Koniges and C. E. Leith, "Parallel
processing
of random number generation for Monte Carlo turbulence
simulation,"
*J. Comput. Phys*., 81: 230-235, 1989. - D. E. Knuth,
*The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Third Edition*, Addison-Wesley, Reading, Massachusetts, 1997. - D. E. Knuth,
*The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Third Edition*, Addison-Wesley, Reading, Massachusetts, 1997. - D. E. Knuth,
*The Art of Computer Programming, Vol. 3: Sorting and Searching, Second Edition*, Addison-Wesley, Reading, Massachusetts, 1998. - N. M. Korobov,
*Exponential Sums and Their Applications*, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992. - R. A. Kronmal and A. V. Peterson Jr., "On
the
Alias Method for Generating Random Variablesom a Discrete
Distribution,"
*The American Statistician*, 33: 214-218, 1979. - L. Kuipers and H. Niederreiter,
*Uniform Distribution of Sequences*, John Wiley and Sons: New York, 1974. - J. C. Lagarias, "Pseudorandom number generators in cryptography and number theory," Proceedings and Symposia in Applied Mathematics (Cryptography and Computational Number Theory), 42: 1-37, Carl Pomerance (ed.), 1990.
- J. C. Lagarias, "Pseudorandom numbers," Statistical Science, 8: 31-39, 1993.
- J. C. Lagarias and V. S. Miller and A. M. Odlyzko, "Computing
*π(x)*: The Meissel-Lehmer method,"*Mathematics of Computation*,**55**: 537-560, 1985. - D. P. Landau and D. Stauffer, "Test of parallel updating in Ising model simulation," Journal de Physique, 50: 509-512, 1989.
- P. L'Ecuyer, "Efficient
and
portable combined random number generators,"
*Comm. of the ACM*,**31**: 742-774, 1988. - P. L'Ecuyer, "Random
numbers
for simulation,"
*Communications of the ACM*,**33**:85-97, 1990. - P. L'Ecuyer, "Uniform
random
number generation,"
*Ann. Oper. Res.*,**53**: 77-120, 1994. - P. L'Ecuyer, and R. Couture, "An
Implementation
of the Lattice and Spectral Tests for Multiple Recursive
Linear Random Number Generators,"
*INFORMS Journal on Computing,***9**: 57-60, 1997. - P. L'Ecuyer, "Random
number
generation," in
*Handbook of Computational Statistics*, J. E. Gentle W. Haerdle and Y. Mori, eds., Springer-Verlag: New York, 2004. - P. L'Ecuyer, "Random
Number
Generation", chapter 3 of
*Elsevier Handbooks in Operations Research and Management Science: Simulation*, S. G. Henderson and B. L. Nelson, eds., Elsevier Science, Amsterdam, pp. 55-81, 2006. - P. L'Ecuyer, "Good
parameter
sets for combined multiple recursive random number generators,"
*Operation Research*,**47**: 169-164, 1999. - P. L'Ecuyer and S. Côté,
"Implementing
a
random number package with splitting facilities ,"
*ACM Transactions on Mathematical Software*,**17(1)**: 98-111, 1991. - P. L'Ecuyer and R. Simard, "TestU01:
A
C Library for Empirical Testing of Random Number Generators,"
*ACM Transactions on Mathematical Software*,**33(4)**: Article 22, 2007. - D. H. Lehmer, "Mathematical methods in large-scale computing
units," in
*Proceedings of the 2nd Symposium on Large-Scale Digital Calculating Machinery*, Harvard University Press: Cambridge, Massachusetts, pp. 141-146, 1949. - A. K. Lenstra, H. W. Lenstra and L. Lovasz, "Factoring polynomials with rational coefficients," Math. Ann., 261: 515-534, 1982.
- T. G. Lewis and W. H. Payne, "Generalized feedback shift register
pseudorandom number algorithms,"
*Journal of the ACM*,**20**: 456-468, 1973. - J. X. Li and G. L. Mullen, "Parallel
computing
of a quasi-Monte Carlo algorithm for valuing derivatives,"
*Parallel Computing*,**26**: 641-653, 2000. - R. Lidl and H. Niederreiter,
*Introduction to Finite Fields and Their Applications*, Cambridge University Press: Cambridge, London, New York, 1986. - R.. Lidl and H. Niederreiter, "Finite Fields," in
*Encyclopedia of Mathematics and Its Applications*, Addison-Wesley: Reading, Massachusetts, 1983. - M. Lüscher,
*"A portable high-quality random number generator for lattice field theory simulations*,"*Comp. Phys. Comm.,***79**: 100-110, 1994. - N. M. MacLaren, "The
generation
of multiple independent sequences of pseudorandom numbers,"
*Applied Statistics*,**38**: 351-359, 1989. - J. Makino, "Lagged-Fibonacci
random
number
generators on parallel computers,"
*Parallel Computing*,**20**: 1357-1367, 1994. - G. Marsaglia, "DIEHARD software package," http://stat.fsu.edu/pub/diehard/
- G. Marsaglia, "Random
numbers
fall mainly in the planes,"
*Proc. Nat. Acad. Sci. U.S.A.*,**62**: 25-28, 1968. - G. Marsaglia, "The structure of linear congruential sequences,"
in
*Applications of Number Theory to Numerical Analysis*, S. K. Zaremba, ed., Academic Press: New York, pp. 249-285, 1972. - G. Marsaglia, "A
current view of random number generators," in
*Computing Science and Statistics: Proceedings of the XVIth Symposium on the Interface*, pp. 3-10, 1985. - G. Marsaglia and T. A. Bray, "A convenient method for generating normal
variables,"
*SIAM Review*,**6**: 260-264, 1964. - G. Marsaglia and L.H. Tsay, "Matrices
and
the structure of random number sequences,"
*Linear Alg. and Applic.*,**67**: 147-156, 1985. - G. Marsaglia and A. Zaman and W. W. Tsang, "Toward a universal random number generator,"
*Statist. Probab. Lett.*,**9**: 35-39, 1990. - G. Marsaglia and A. Zaman, "A new class of random number generators,"
*The Annals of Applied Probability*,**1**: 462-480, 1991. - O. Martin and A. M. Odlyzko and S. Wolfram, "Algebraic properties of cellular automata,"
*Comm. Math. Phys*.,**93**: 219-258, 1984. - M. Mascagni, "Random
Number
Generation," in
*CRC Standard Mathematical Tables and Formulae 31st Edition*, D. Zwillinger, editor, Chapman and Hall/CRC, Boca Raton, pp. 644-649, 2003. - M. Mascagni, "Deterministic
Monte
Carlo
Methods and Parallelism,"
*Sourcebook on Parallel Computing*, J. Dongarra, I. Foster, F. Fox, W. Gropp, K. Kennedy, L. Torcson, and A. White, editors, Morgan Kaufman Publishers, San Francisco, pp. 249-258, 2003. - M. Mascagni and S. A. Cuccaro and D. V. Pryor and M. L.
Robinson, "Recent
Developments
in Parallel Pseudorandom Number Generation," in
*Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing*, volume II, D. E. Keyes and M. R. Leuze and L. R. Petzold and D. A. Reed, eds., SIAM: Philadelphia, Pennsylvania, pp. 524-529, 1993. - M. Mascagni and M. L. Robinson and D. V. Pryor and S. A.
Cuccaro, "Parallel
pseudorandom
number generation using additive lagged-Fibonacci recursions,"
*Lecture Notes in Statistics*,**106**: 263-277, 1995. - M. Mascagni and S. A. Cuccaro and D. V. Pryor and M. L.
Robinson, "A
fast, high-quality, and reproducible lagged-Fibonacci
pseudorandom number generator,"
*J. Comput. Physics*, 15: 211-219. 1995. - M. Mascagni, "Parallel
linear
congruential
generators with prime moduli,"
*Parallel Computing,***24**: 923-936, 1998. - M. Mascagni, "Some methods of parallel pseudorandom number generation," in Proceedings of the IMA Workshop on Algorithms for Parallel Processing, R. Schreiber, M. Heath and A. Ranade, eds., Springer-Verlag: New York, Berlin, pp. 277-288, 1999.
- M. Mascagni, "Parallel
Pseudorandom
Number
Generation,"
*SIAM News*,**August**, pp. 1,8-10, 1999. - M. Mascagni, "Serial
and
Parallel Random Number Generation," in
*Quantum Monte Carlo in Physics and Chemistry*, NATO ASI Series, Series C: Mathematical and Physical Sciences, Peter Nightingale and Cyrus Umrigar, eds., Kluwer: Dordrecht, pp. 425-446, 1999. - M. Mascagni and J. Ren, "New Development in the Scalable
Parallel Random Number Generator (SPRNG) Library,"
*The Institute of Statistical Mathematics Cooperative Research Report,***210:**120-125, 2008. - M. Mascagni and A. Srinivasan, "Parameterizing
Parallel
Multiplicative Lagged-Fibonacci Generators,"
*Parallel Computing*,**30**: 899-916, 2004. - M. Mascagni and A. Srinivasan, "Algorithm
806:
SPRNG: A Scalable Library for Pseudorandom Number Generation,"
*ACM Transactions on Mathematical Software*,**26**: 436-461, 2000. - M. Mascagni and H. Chi, "Parallel
linear
congruential generators with Sophie-Germain moduli," Parallel Computing, 30(11): 1217-1231, 2004.

- J. L. Massey, "Shift-register synthesis and BCH decoding,"
*IEEE Trans. Information Theory*, 15: 122-127, 1969, - N. Masuda and F. Zimmermann, "PRNGlib: A parallel random number generator library," Swiss Center for Scientific Computing Technical Report: TR-96-08, 1996.
- Makoto Matsumoto and Takuji
Nishimura, "Dynamic
Creation
of Pseudorandom Number Generators",

Monte Carlo and Quasi-Monte Carlo Methods 1998, Springer, pp 56-69, 2000. - M. Matsumoto and Y. Kurita, "Twisted
GFSR
generators,"
*ACM Trans. Model. Comput. Simul.*,**2**: 179-194, 1992. - M. Matsumoto and T. Nishimura, "Mersenne
twister:
A 623-dimensionally equidistributed uniform pseudo-random
number generator,"
*ACM Trans. Model. Comput. Simul.*, 8: 3-30, 1998. - W. J. Morokoff and R. E. Caflisch, "Quasi-random
sequences
and their discrepancies," SIAM Journal on Scientific
Computing,
**15(6)**: 1251-1279, 1994. - W. J. Morokoff and R. E. Caflisch, "Quasi-Monte
Carlo integration,"
*J. Comp. Phys.*,**122**: 218-230, 1995. - H. R. Neave, "On
using
the Box-Muller transformation with multiplicative congruential
pseudo-random number generators,"
*Appl. Statist.*,**22**: 92-97, 1973. - H. Niederreiter, "Quasi-Monte
Carlo
methods
and pseudo-random numbers,"
*Bull. Amer. Math. Soc.*,**84**: 957-1041, 1978. - H. Niederreiter, "The
serial
test for pseudo-random numbers generated by the linear
congruential method,"
*Numer. Math.*,**46**: 51-68, 1985. - H. Niederreiter, "A
statistical analysis of generalized feedback shift register
pseudorandom number generators,"
*SIAM J. Sci. Stat. Comput.*,**8**: 1035-1051, 1987. - H. Niederreiter, "Point
sets
and sequences with small discrepancy,"
*Montash. Math.*,**103**: 269-288, 1987. - H. Niederreiter, "The
serial
test for digital
*k*-step pseudorandom numbers,"*Math. J. Okayama Univ.*,**30**: 93-119, 1988. - H. Niederreiter, "Remarks
on
nonlinear congruential pseudorandom numbers,"
*Metrika*,**35**: 321-328, 1988. - H. Niederreiter, "Statistical
independence
of nonlinear congruential pseudorandom numbers,"
*Montash. Math.*,**106**: 149-159, 1988. - H. Niederreiter, "Low-discrepancy and low-dispersion sequences,"
*J. Number Theory*,**30**: 51-70, 1988. - H. Niederreiter, "The
serial
test for congruential pseudorandom numbers generated by
inversion,"
*Math. Comput.*,**52**: 125-144, 1989. - H. Niederreiter, "Pseudorandom
numbers
generated from shift register sequences",
*Lecture Notes in Math.*,**1452**: 165-177, 1990. - H. Niederreiter, "Statistical
independence
properties of pseudorandom vectors produced by matrix
generators,"
*J. Comput. and Appl. Math.*,**31**: 139-151, 1990. - H. Niederreiter, "Lower
bounds
for the discrepancy of inversive congruential pseudorandom
numbers",
*Math. Comput.*,**55**: 277-287, 1990. - H. Niederreiter, "Recent
trends
in random number and random vector generation,"
*Ann. Oper. Res.*,**31**: 323-36, 1991. - H. Niederreiter, "Random Number Generation and Quasi-Monte Carlo Methods," SIAM: Philadelphia, Pennsylvania, 1992. (Book review)
- H. Niederreiter, "Factorization
of
polynomials and some linear-algebra problems over finite
fields", Linear Algebra and Its Appl. 192, 301-328, 1993.

- H. Niederreiter, "On
a
new class of pseudorandom numbers for simulation methods,"
*J. Comput. Appl. Math.*,**56**: 159-167, 1994. - H. Niederreiter and I. E. Shparlinski, "Recent
advances
in the theory of nonlinear pseudorandom number generators," in: K.T. Fang, F.
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