Constructions of digital nets

Acta Arithmetica

Volumn 102, Issue 2, 2002, Pages 189-197

  Niederreiter, Harald ^a,b   Xing, Chaoping ^a,b,c  

^a National University of Singapore ^*

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044532627     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa102-2-7     Document Type: Review

References (16)

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2. _, _, Families of ternary (t, m, s)-nets related to BCH-codes, Monatsh. Math. 132 (2001), 99-103.
3. R. Hill, A First Course in Coding Theory, Oxford Univ. Press, Oxford, 1986.
4. K. M. Lawrence, A. Mahalanabis, G. L. Mullen and W. C. Schmid, Construction of digital (t, m, s)-nets from linear codes, in: Finite Fields and Applications, S. Cohen and H. Niederreiter (eds.), London Math. Soc. Lecture Note Ser. 233, Cambridge Univ. Press, Cambridge, 1996, 189-208.
5. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, rev. ed., Cambridge Univ. Press, Cambridge, 1994.
6. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
7. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
8. _, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
9. H. Niederreiter, Constructions of (t, m, s)-nets, in: Monte Carlo and Quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier (eds.), Springer, Berlin, 2000, 70-85.
10. H. Niederreiter and G. Pirsic, Duality for digital nets and its applications, Acta Arith. 97 (2001), 173-182.
11. H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
12. _, _, Rational Points on Curves over Finite Fields: Theory and Applications, London Math. Soc. Lecture Note Ser. 285, Cambridge Univ. Press, Cambridge, 2001.
13. _, _, A construction of digital nets with good asymptotic behavior, preprint, 2001.
14. G. Pirsic, Base changes for (t, m, s)-nets and related sequences, Sitzungsber. Österr. Akad. Wiss. Math.-Naturw. Kl. Abt. II 208 (1999), 115-122.
15. W. C. Schmid and R. Wolf, Bounds for digital nets and sequences, Acta Arith. 78 (1997), 377-399.
16. J. H. van Lint, Introduction to Coding Theory, 3rd ed., Springer, Berlin, 2000.