Article
MSC:
11K38,
11K45,
11Y99,
65C05,
65D30 | MR 1152177 | Zbl 0757.11024 | DOI: 10.21136/CMJ.1992.128322
Full entry |
PDF
(2.5 MB)
Feedback
PDF
(2.5 MB)
Feedback
References:
[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 10.2307/2008509 | MR 1011436
[2] M. Car: Sommes de carrés dans $F_{q}[X]$. Dissertationes Math. 215 (1983). MR 0718932
[3] L. Carlitz: The arithmetic of polynomials in a Galois field. Amer. J. Math. 54 (1932), 39–50. DOI 10.2307/2371075 | MR 1506871 | Zbl 0003.19502
[4] L. Carlitz: The singular series for sums of squares of polynomials. Duke Math. J. 14 (1947), 1105–1120. DOI 10.1215/S0012-7094-47-01484-1 | MR 0023304 | Zbl 0032.00204
[5] H. Faure: Discrépance de suites associées à un système de numération (en dimension $s$). Acta Arith. 41 (1982), 337–351. DOI 10.4064/aa-41-4-337-351 | MR 0677547 | Zbl 0442.10035
[6] D. R. Hayes: The expression of a polynomial as a sum of three irreducibles. Acta Arith. 11 (1966), 461–488. DOI 10.4064/aa-11-4-461-488 | MR 0201422 | Zbl 0151.03902
[7] L. K. Hua and Y. Wang: Applications of Number Theory to Numerical Analysis. (1981), Springer, Berlin. MR 0617192
[8] R. Lidl and H. Niederreiter: Finite Fields. Addison-Wesley, Reading, MA, 1983. MR 0746963
[9] G. L. Mullen and H. Niederreiter: Optimal characteristic polynomials for digital multistep pseudorandom numbers. Computing 39 (1987), 155–163. DOI 10.1007/BF02310104 | MR 0919665
[10] H. Niederreiter: On the distribution of pseudorandom numbers generated by the linear congruential method. III. Math. Comp. 30 (1976), 571–597. DOI 10.1090/S0025-5718-1976-0457392-1 | MR 0457392
[11] H. Niederreiter: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. 84 (1978), 957–1041. DOI 10.1090/S0002-9904-1978-14532-7 | MR 0508447 | Zbl 0404.65003
[12] H. Niederreiter: Low-discrepancy point sets. Monatsh. Math. 102 (1986), 155–167. DOI 10.1007/BF01490206 | MR 0861937 | Zbl 0584.10034
[13] H. Niederreiter: Pseudozufallszahlen und die Theorie der Gleichverteilung. Sitzungsber. Osterr. Akad. Wiss. Math.-Naturwiss. Kl. Abt. II 195 (1986), 109–138. MR 0881335 | Zbl 0616.10040
[14] H. Niederreiter: Rational functions with partial quotients of small degree in their continued fraction expansion. Monatsh. Math. 103 (1987), 269–288. DOI 10.1007/BF01318069 | MR 0897953 | Zbl 0624.12011
[15] H. Niederreiter: A statistical analysis of generalized feedback shift register pseudorandom number generators. SIAM J. Sci. Statist. Computing 8 (1987), 1035–1051. DOI 10.1137/0908084 | MR 0911073 | Zbl 0634.65003
[16] H. Niederreiter: Point sets and sequences with small discrepancy. Monatsh. Math. 104 (1987), 273–337. DOI 10.1007/BF01294651 | MR 0918037 | Zbl 0626.10045
[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 1021532 | Zbl 0662.65021
[18] H. Niederreiter: Low-discrepancy and low-dispersion sequences. J. Number Theory 30 (1988), 51–70. DOI 10.1016/0022-314X(88)90025-X | MR 0960233 | Zbl 0651.10034
[19] H. Niederreiter: A combinatorial problem for vector spaces over finite fields. Discrete Math. (to appear). MR 1139449 | Zbl 0747.11063
[20] W. M. Schmidt: Irregularities of distribution. VII. Acta Arith. 21 (1972), 45–50. DOI 10.4064/aa-21-1-45-50 | MR 0319933 | Zbl 0244.10035
[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 0219238 | Zbl 0185.41103
[22] S. Tezuka: A new family of low-discrepancy point sets, Tech.
Search
Partner of
