A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators
Gerhard Larcher
Acta Arithmetica, Tome 84 (1998), p. 1-15 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207103 
@article{bwmeta1.element.bwnjournal-article-aav83i1p1bwm,
     author = {Gerhard Larcher},
     title = {A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {1-15},
     zbl = {0885.11050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav83i1p1bwm}
}

Gerhard Larcher. A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators. Acta Arithmetica, Tome 84 (1998) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav83i1p1bwm/

[000] [1] T. G. Lewis and W. H. Payne, Generalized feedback shift register pseudorandom number algorithm, J. Assoc. Comput. Mach. 20 (1973), 456-468. | Zbl 0266.65009

[001] [2] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. | Zbl 0626.10045

[002] [3] H. Niederreiter, The serial test for digital k-step pseudorandom numbers, Math. J. Okayama Univ. 30 (1988), 93-119. | Zbl 0666.65003

[003] [4] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conf. Ser. in Appl. Math. 63, SIAM, Philadelphia, 1992.

[004] [5] H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328. | Zbl 0845.11042

[005] [6] H. Niederreiter, The multiple recursive matrix method for pseudorandom number generation, Finite Fields Appl. 1 (1995), 3-30. | Zbl 0823.11041

[006] [7] H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225-240. | Zbl 0893.11031

[007] [8] H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298. | Zbl 0833.11035

[008] [9] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.

[009] [10] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: S. Cohen and H. Niederreiter (eds.), Finite Fields and Applications (Glasgow, 1995), London Math. Soc. Lecture Note Ser. 233, Cambridge Univ. Press, Cambridge, 1996, 269-296. | Zbl 0932.11050

[010] [11] K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79. | Zbl 0057.28604

[011] [12] W. M. Schmidt, Irregularities of distribution, VII, Acta Arith. 21 (1972), 45-50. | Zbl 0244.10035

[012] [13] R. C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201-209. | Zbl 0137.34804