Low-discrepancy sequences obtained from algebraic function fields over finite fields

• Autorzy: Harald Niederreiter , Chaoping Xing
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 72
• Numer: 3
• Strony: 281-298

Daty

wydano

1995

otrzymano

1995-01-24

Twórcy

autor

Harald Niederreiter

• Institut für Informationsverarbeitung, Österreichische Akademie, der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria

autor

Chaoping Xing

• Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Bibliografia

• [1] P. Bratley, B. L. Fox and H. Niederreiter, Implementation and tests of low-discrepancy sequences, ACM Trans. Model. Comput. Simulation 2 (1992), 195-213.
• [2] H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351.
• [3] G. Larcher, H. Niederreiter and W. C. Schmid, Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration, Monatsh. Math., to appear.
• [4] G. Larcher and W. C. Schmid, Multivariate Walsh series, digital nets and quasi-Monte Carlo integration, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue (eds.), Lecture Notes in Statist., Springer, Berlin, to appear.
• [5] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge Univ. Press, Cambridge, 1994.
• [6] G. L. Mullen, A. Mahalanabis and H. Niederreiter, Tables of (t,m,s)-net and (t,s)-sequence parameters, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue (eds.), Lecture Notes in Statist., Springer, Berlin, to appear.
• [7] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
• [8] H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70.
• [9] H. Niederreiter, A combinatorial problem for vector spaces over finite fields, Discrete Math. 96 (1991), 221-228.
• [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992.
• [11] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652.
• [12] H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328.
• [13] 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 (in Russian).
• [14] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.