| Title:
|
Low-discrepancy point sets obtained by digital constructions over finite fields (English) |
| Author:
|
Niederreiter, Harald |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
143-166 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11K38 |
| MSC:
|
11K45 |
| MSC:
|
11Y99 |
| MSC:
|
65C05 |
| MSC:
|
65D30 |
| idZBL:
|
Zbl 0757.11024 |
| idMR:
|
MR1152177 |
| DOI:
|
10.21136/CMJ.1992.128322 |
| . |
| Date available:
|
2009-09-24T09:18:01Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128322 |
| . |
| Reference:
|
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| Reference:
|
[2] M. Car: Sommes de carrés dans $F_{q}[X]$.Dissertationes Math. 215 (1983). MR 0718932 |
| Reference:
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[3] L. Carlitz: The arithmetic of polynomials in a Galois field.Amer. J. Math. 54 (1932), 39–50. Zbl 0003.19502, MR 1506871, 10.2307/2371075 |
| Reference:
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[4] L. Carlitz: The singular series for sums of squares of polynomials.Duke Math. J. 14 (1947), 1105–1120. Zbl 0032.00204, MR 0023304, 10.1215/S0012-7094-47-01484-1 |
| Reference:
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[5] H. Faure: Discrépance de suites associées à un système de numération (en dimension $s$).Acta Arith. 41 (1982), 337–351. Zbl 0442.10035, MR 0677547, 10.4064/aa-41-4-337-351 |
| Reference:
|
[6] D. R. Hayes: The expression of a polynomial as a sum of three irreducibles.Acta Arith. 11 (1966), 461–488. Zbl 0151.03902, MR 0201422, 10.4064/aa-11-4-461-488 |
| Reference:
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[7] L. K. Hua and Y. Wang: Applications of Number Theory to Numerical Analysis.(1981), Springer, Berlin. MR 0617192 |
| Reference:
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[8] R. Lidl and H. Niederreiter: Finite Fields.Addison-Wesley, Reading, MA, 1983. MR 0746963 |
| Reference:
|
[9] G. L. Mullen and H. Niederreiter: Optimal characteristic polynomials for digital multistep pseudorandom numbers.Computing 39 (1987), 155–163. MR 0919665, 10.1007/BF02310104 |
| Reference:
|
[10] H. Niederreiter: On the distribution of pseudorandom numbers generated by the linear congruential method. III.Math. Comp. 30 (1976), 571–597. MR 0457392, 10.1090/S0025-5718-1976-0457392-1 |
| Reference:
|
[11] H. Niederreiter: Quasi-Monte Carlo methods and pseudo-random numbers.Bull. Amer. Math. Soc. 84 (1978), 957–1041. Zbl 0404.65003, MR 0508447, 10.1090/S0002-9904-1978-14532-7 |
| Reference:
|
[12] H. Niederreiter: Low-discrepancy point sets.Monatsh. Math. 102 (1986), 155–167. Zbl 0584.10034, MR 0861937, 10.1007/BF01490206 |
| Reference:
|
[13] H. Niederreiter: Pseudozufallszahlen und die Theorie der Gleichverteilung.Sitzungsber. Osterr. Akad. Wiss. Math.-Naturwiss. Kl. Abt. II 195 (1986), 109–138. Zbl 0616.10040, MR 0881335 |
| Reference:
|
[14] H. Niederreiter: Rational functions with partial quotients of small degree in their continued fraction expansion.Monatsh. Math. 103 (1987), 269–288. Zbl 0624.12011, MR 0897953, 10.1007/BF01318069 |
| Reference:
|
[15] H. Niederreiter: A statistical analysis of generalized feedback shift register pseudorandom number generators.SIAM J. Sci. Statist. Computing 8 (1987), 1035–1051. Zbl 0634.65003, MR 0911073, 10.1137/0908084 |
| Reference:
|
[16] H. Niederreiter: Point sets and sequences with small discrepancy.Monatsh. Math. 104 (1987), 273–337. Zbl 0626.10045, MR 0918037, 10.1007/BF01294651 |
| Reference:
|
[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. Zbl 0662.65021, MR 1021532 |
| Reference:
|
[18] H. Niederreiter: Low-discrepancy and low-dispersion sequences.J. Number Theory 30 (1988), 51–70. Zbl 0651.10034, MR 0960233, 10.1016/0022-314X(88)90025-X |
| Reference:
|
[19] H. Niederreiter: A combinatorial problem for vector spaces over finite fields.Discrete Math. (to appear). Zbl 0747.11063, MR 1139449 |
| Reference:
|
[20] W. M. Schmidt: Irregularities of distribution. VII.Acta Arith. 21 (1972), 45–50. Zbl 0244.10035, MR 0319933, 10.4064/aa-21-1-45-50 |
| Reference:
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[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) Zbl 0185.41103, MR 0219238 |
| Reference:
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[22] S. Tezuka: A new family of low-discrepancy point sets, Tech... |
| . |
