@article{10_21136_CMJ_1992_128322,
author = {Niederreiter, Harald},
title = {Low-discrepancy point sets obtained by digital constructions over finite fields},
journal = {Czechoslovak Mathematical Journal},
pages = {143--166},
year = {1992},
volume = {42},
number = {1},
doi = {10.21136/CMJ.1992.128322},
mrnumber = {1152177},
zbl = {0757.11024},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1992.128322/}
}
TY - JOUR AU - Niederreiter, Harald TI - Low-discrepancy point sets obtained by digital constructions over finite fields JO - Czechoslovak Mathematical Journal PY - 1992 SP - 143 EP - 166 VL - 42 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1992.128322/ DO - 10.21136/CMJ.1992.128322 LA - en ID - 10_21136_CMJ_1992_128322 ER -
%0 Journal Article %A Niederreiter, Harald %T Low-discrepancy point sets obtained by digital constructions over finite fields %J Czechoslovak Mathematical Journal %D 1992 %P 143-166 %V 42 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1992.128322/ %R 10.21136/CMJ.1992.128322 %G en %F 10_21136_CMJ_1992_128322
Niederreiter, Harald. Low-discrepancy point sets obtained by digital constructions over finite fields. Czechoslovak Mathematical Journal, Tome 42 (1992) no. 1, pp. 143-166. doi: 10.21136/CMJ.1992.128322
[1] D. A. André, G. L. Mullen, and H. Niederreiter: Figures of merit for digital multistep pseudorandom numbers. Math. Comp. 54 (1990), 737–748. | DOI | MR
[2] M. Car: Sommes de carrés dans $F_{q}[X]$. Dissertationes Math. 215 (1983). | MR
[3] L. Carlitz: The arithmetic of polynomials in a Galois field. Amer. J. Math. 54 (1932), 39–50. | DOI | MR | Zbl
[4] L. Carlitz: The singular series for sums of squares of polynomials. Duke Math. J. 14 (1947), 1105–1120. | DOI | MR | Zbl
[5] H. Faure: Discrépance de suites associées à un système de numération (en dimension $s$). Acta Arith. 41 (1982), 337–351. | DOI | MR | Zbl
[6] D. R. Hayes: The expression of a polynomial as a sum of three irreducibles. Acta Arith. 11 (1966), 461–488. | DOI | MR | Zbl
[7] L. K. Hua and Y. Wang: Applications of Number Theory to Numerical Analysis. (1981), Springer, Berlin. | MR
[8] R. Lidl and H. Niederreiter: Finite Fields. Addison-Wesley, Reading, MA, 1983. | MR
[9] G. L. Mullen and H. Niederreiter: Optimal characteristic polynomials for digital multistep pseudorandom numbers. Computing 39 (1987), 155–163. | DOI | MR
[10] H. Niederreiter: On the distribution of pseudorandom numbers generated by the linear congruential method. III. Math. Comp. 30 (1976), 571–597. | DOI | MR
[11] H. Niederreiter: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. 84 (1978), 957–1041. | DOI | MR | Zbl
[12] H. Niederreiter: Low-discrepancy point sets. Monatsh. Math. 102 (1986), 155–167. | DOI | MR | Zbl
[13] H. Niederreiter: Pseudozufallszahlen und die Theorie der Gleichverteilung. Sitzungsber. Osterr. Akad. Wiss. Math.-Naturwiss. Kl. Abt. II 195 (1986), 109–138. | MR | Zbl
[14] H. Niederreiter: Rational functions with partial quotients of small degree in their continued fraction expansion. Monatsh. Math. 103 (1987), 269–288. | DOI | MR | Zbl
[15] H. Niederreiter: A statistical analysis of generalized feedback shift register pseudorandom number generators. SIAM J. Sci. Statist. Computing 8 (1987), 1035–1051. | DOI | MR | Zbl
[16] H. Niederreiter: Point sets and sequences with small discrepancy. Monatsh. Math. 104 (1987), 273–337. | DOI | MR | Zbl
[17] H. Niederreiter: Quasi-Monte Carlo methods for multidimensional numerical integration. Numerical Integration III (Oberwolfach 1987), Internat. Series of Numer. Math., Vol. 85, Birkhäuser, Basel, 1988, pp. 157–171. | MR | Zbl
[18] H. Niederreiter: Low-discrepancy and low-dispersion sequences. J. Number Theory 30 (1988), 51–70. | DOI | MR | Zbl
[19] H. Niederreiter: A combinatorial problem for vector spaces over finite fields. Discrete Math. (to appear). | MR | Zbl
[20] W. M. Schmidt: Irregularities of distribution. VII. Acta Arith. 21 (1972), 45–50. | DOI | MR | Zbl
[21] I. M. Sobol’: The distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967), 784–802. (Russian) | MR | Zbl
[22] S. Tezuka: A new family of low-discrepancy point sets, Tech.
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