메뉴 건너뛰기




Volumn 11, Issue 3, 2005, Pages 578-600

Constructions of (t, m, s)-net and (t, s)-sequences

Author keywords

Digital (t, s) sequence; Digital net; Duality theory for digital nets; Net, (t, s) sequence; Ordered orthogonal array; Polynomial lattice; Quasi Monte Carlo method; Scrambled (t, s) sequence; Scrambled net

Indexed keywords

COMBINATORIAL MATHEMATICS; LINEAR EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MONTE CARLO METHODS; POLYNOMIALS; PROBABILITY; THEOREM PROVING;

EID: 23044461865     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ffa.2005.01.001     Document Type: Article
Times cited : (53)

References (80)
  • 1
    • 23044505151 scopus 로고    scopus 로고
    • A new efficient algorithm for generating the scrambled Sobol' sequence
    • I. Dimov, I. Lirkov, S. Margenov, Z. Zlatev (Eds.) Lecture Notes in Computer Science Springer, Berlin
    • E.I. Atanassov, A new efficient algorithm for generating the scrambled Sobol' sequence, in: I. Dimov, I. Lirkov, S. Margenov, Z. Zlatev (Eds.), Numerical Methods and Applications, Lecture Notes in Computer Science, vol. 2542, Springer, Berlin, 2003, pp. 83-90.
    • (2003) Numerical Methods and Applications , vol.2542 , pp. 83-90
    • Atanassov, E.I.1
  • 2
    • 3142724271 scopus 로고    scopus 로고
    • Coding-theoretic constructions for (t, m, s)-nets and ordered orthogonal arrays
    • J. Bierbrauer Y. Edel W.Ch. Schmid Coding-theoretic constructions for (t, m, s) -nets and ordered orthogonal arrays J. Combin. Designs 10 2002 403-418
    • (2002) J. Combin. Designs , vol.10 , pp. 403-418
    • Bierbrauer, J.1    Edel, Y.2    Schmid, W.Ch.3
  • 4
    • 0002350694 scopus 로고    scopus 로고
    • Applications of combinatorial designs to communications, cryptography, and networking
    • J.D. Lamb, D.A. Preece (Eds.) London Mathematical Society, Lecture Note Series Cambridge University Press, Cambridge
    • C.J. Colbourn, J.H. Dinitz, D.R. Stinson, Applications of combinatorial designs to communications, cryptography, and networking, in: J.D. Lamb, D.A. Preece (Eds.), Surveys in Combinatorics 1999, London Mathematical Society, Lecture Note Series, vol. 267, Cambridge University Press, Cambridge, 1999, pp. 37-100.
    • (1999) Surveys in Combinatorics 1999 , vol.267 , pp. 37-100
    • Colbourn, C.J.1    Dinitz, J.H.2    Stinson, D.R.3
  • 5
    • 2142786713 scopus 로고    scopus 로고
    • The number of linearly independent binary vectors with applications to the construction of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes
    • S.B. Damelin G. Michalski G.L. Mullen D. Stone The number of linearly independent binary vectors with applications to the construction of hypercubes and orthogonal arrays, pseudo (t, m, s) -nets and linear codes Monatsh. Math. 141 2004 277-288
    • (2004) Monatsh. Math. , vol.141 , pp. 277-288
    • Damelin, S.B.1    Michalski, G.2    Mullen, G.L.3    Stone, D.4
  • 6
    • 23044436120 scopus 로고    scopus 로고
    • Construction algorithms for polynomial lattice rules for multivariate integration
    • to appear
    • J. Dick, F.Y. Kuo, F. Pillichshammer, I.H. Sloan, Construction algorithms for polynomial lattice rules for multivariate integration, Math. Comp., to appear.
    • Math. Comp.
    • Dick, J.1    Kuo, F.Y.2    Pillichshammer, F.3    Sloan, I.H.4
  • 7
    • 23044446160 scopus 로고    scopus 로고
    • Weighted star discrepancy of digital nets in prime bases
    • preprint
    • J. Dick, H. Niederreiter, F. Pillichshammer, Weighted star discrepancy of digital nets in prime bases, preprint, 2004.
    • (2004)
    • Dick, J.1    Niederreiter, H.2    Pillichshammer, F.3
  • 9
    • 23944495195 scopus 로고    scopus 로고
    • Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
    • to appear
    • J. Dick, F. Pillichshammer, Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces, J. Complexity, to appear.
    • J. Complexity
    • Dick, J.1    Pillichshammer, F.2
  • 10
    • 0039840000 scopus 로고    scopus 로고
    • Families of ternary (t, m, s)-nets related to BCH-codes
    • Y. Edel J. Bierbrauer Families of ternary (t, m, s)-nets related to BCH-codes Monatsh. Math. 132 2001 99-103
    • (2001) Monatsh. Math. , vol.132 , pp. 99-103
    • Edel, Y.1    Bierbrauer, J.2
  • 11
    • 0035704436 scopus 로고    scopus 로고
    • Variations on (0, s)-sequences
    • H. Faure Variations on (0, s)-sequences J. Complexity 17 2001 741-753
    • (2001) J. Complexity , vol.17 , pp. 741-753
    • Faure, H.1
  • 12
    • 0008854038 scopus 로고    scopus 로고
    • Another random scrambling of digital (t, s)-sequences
    • K.-T. Fang F.J. Hickernell H. Niederreiter (eds.) Springer Berlin
    • H. Faure S. Tezuka Another random scrambling of digital (t, s) -sequences in K.-T. Fang F.J. Hickernell H. Niederreiter (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000 2002 Springer Berlin 242-256
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 242-256
    • Faure, H.1    Tezuka, S.2
  • 13
    • 0037417035 scopus 로고    scopus 로고
    • The quality parameter for digital (t, m, s)-nets
    • M.E. Flahive The quality parameter for digital (t, m, s)-nets Math. Comp. Simulation 62 2003 327-333
    • (2003) Math. Comp. Simulation , vol.62 , pp. 327-333
    • Flahive, M.E.1
  • 14
    • 0037948430 scopus 로고    scopus 로고
    • Strategies for Quasi-Monte Carlo
    • Boston: Kluwer Academic Publishers
    • B.L. Fox Strategies for Quasi-Monte Carlo 1999 Kluwer Academic Publishers Boston
    • (1999)
    • Fox, B.L.1
  • 15
    • 0003378660 scopus 로고    scopus 로고
    • Fast generation of randomized low-discrepancy point sets
    • K.-T. Fang F.J. Hickernell H. Niederreiter (eds.) Springer Berlin
    • I. Friedel A. Keller Fast generation of randomized low-discrepancy point sets in K.-T. Fang F.J. Hickernell H. Niederreiter (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000 2002 Springer Berlin 257-273
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 257-273
    • Friedel, I.1    Keller, A.2
  • 16
    • 0004344974 scopus 로고    scopus 로고
    • Tables of curves with many points
    • available at
    • G. van der Geer, M. van der Vlugt, Tables of curves with many points, available at http://www.science.uva.nl/~geer/tables-mathcomp14.ps.
    • van der Geer, G.1    van der Vlugt, M.2
  • 17
    • 0041331599 scopus 로고    scopus 로고
    • Digital (t, m, s)-nets and the spectral test
    • P. Hellekalek Digital (t, m, s)-nets and the spectral test Acta Arith. 105 2002 197-204
    • (2002) Acta Arith. , vol.105 , pp. 197-204
    • Hellekalek, P.1
  • 18
    • 84867923529 scopus 로고    scopus 로고
    • Hypercubic 4- and 5-designs from double-error-correcting BCH codes
    • T. Helleseth T. Kløve V.I. Levenshtein Hypercubic 4- and 5-designs from double-error-correcting BCH codes Designs Codes Cryptogr. 28 2003 265-282
    • (2003) Designs Codes Cryptogr. , vol.28 , pp. 265-282
    • Helleseth, T.1    Kløve, T.2    Levenshtein, V.I.3
  • 20
    • 0038934825 scopus 로고    scopus 로고
    • The asymptotic efficiency of randomized nets for quadrature
    • F.J. Hickernell H.S. Hong The asymptotic efficiency of randomized nets for quadrature Math. Comp. 68 1999 767-791
    • (1999) Math. Comp. , vol.68 , pp. 767-791
    • Hickernell, F.J.1    Hong, H.S.2
  • 21
    • 0034432296 scopus 로고    scopus 로고
    • The mean square discrepancy of scrambled (t, s)-sequences
    • F.J. Hickernell R.X. Yue The mean square discrepancy of scrambled (t, s) -sequences SIAM J. Numer. Anal. 38 2001 1089-1112
    • (2001) SIAM J. Numer. Anal. , vol.38 , pp. 1089-1112
    • Hickernell, F.J.1    Yue, R.X.2
  • 22
    • 23044492102 scopus 로고    scopus 로고
    • Digital nets and sequences for quasi-Monte Carlo methods
    • Ph.D. Thesis, Hong Kong Baptist University
    • H.S. Hong, Digital nets and sequences for quasi-Monte Carlo methods, Ph.D. Thesis, Hong Kong Baptist University, 2002.
    • (2002)
    • Hong, H.S.1
  • 23
    • 1842651631 scopus 로고    scopus 로고
    • Algorithm 823: Implementing scrambled digital sequences
    • H.S. Hong F.J. Hickernell Algorithm 823: Implementing scrambled digital sequences ACM Trans. Math. Software 29 2003 95-109
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 95-109
    • Hong, H.S.1    Hickernell, F.J.2
  • 25
    • 0001356123 scopus 로고    scopus 로고
    • Digital points sets: Analysis and application
    • P. Hellekalek, G. Larcher (Eds.) Lecture Notes in Statistics Springer, New York
    • G. Larcher, Digital points sets: Analysis and application, in: P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Lecture Notes in Statistics, vol. 138, Springer, New York, 1998, pp. 167-222.
    • (1998) Random and Quasi-Random Point Sets , vol.138 , pp. 167-222
    • Larcher, G.1
  • 26
    • 0000037076 scopus 로고    scopus 로고
    • Construction of digital (t, m, s) -nets from linear codes
    • S. Cohen, H. Niederreiter (Eds.) London Mathematical Society, Lecture Note Series Cambridge University Press, Cambridge 1996
    • K.M. Lawrence, A. Mahalanabis, G.L. Mullen, W.Ch. Schmid, Construction of digital (t, m, s)-nets from linear codes, in: S. Cohen, H. Niederreiter (Eds.), Finite Fields and Applications, London Mathematical Society, Lecture Note Series, vol. 233, Cambridge University Press, Cambridge, 1996, pp. 189-208.
    • Finite Fields and Applications , vol.233 , pp. 189-208
    • Lawrence, K.M.1    Mahalanabis, A.2    Mullen, G.L.3    Schmid, W.Ch.4
  • 27
    • 0003727566 scopus 로고    scopus 로고
    • Discrete Mathematics Using Latin Squares
    • New York: Wiley
    • C.F. Laywine G.L. Mullen Discrete Mathematics Using Latin Squares 1998 Wiley New York
    • (1998)
    • Laywine, C.F.1    Mullen, G.L.2
  • 28
    • 0142138271 scopus 로고    scopus 로고
    • A hierarchy of complete orthogonal structures
    • C.F. Laywine G.L. Mullen A hierarchy of complete orthogonal structures Ars Combin. 63 2002 75-88
    • (2002) Ars Combin. , vol.63 , pp. 75-88
    • Laywine, C.F.1    Mullen, G.L.2
  • 29
    • 23044496255 scopus 로고    scopus 로고
    • Polynomial integration lattices
    • H. Niederreiter (ed.) Springer Berlin
    • P. L'Ecuyer Polynomial integration lattices in H. Niederreiter (ed) Monte Carlo and Quasi-Monte Carlo Methods 2002 2004 Springer Berlin 73-98
    • (2004) Monte Carlo and Quasi-Monte Carlo Methods 2002 , pp. 73-98
    • L'Ecuyer, P.1
  • 31
    • 0141975228 scopus 로고    scopus 로고
    • Randomized polynomial lattice rules for multivariate integration and simulation
    • C. Lemieux P. L'Ecuyer Randomized polynomial lattice rules for multivariate integration and simulation SIAM J. Sci. Comput. 24 2003 1768-1789
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1768-1789
    • Lemieux, C.1    L'Ecuyer, P.2
  • 32
    • 23044457651 scopus 로고    scopus 로고
    • Linear programming bounds for ordered orthogonal arrays and (t, m, s) -nets
    • H. Niederreiter J. Spanier (ed) Springer Berlin
    • W.J. Martin Linear programming bounds for ordered orthogonal arrays and (t, m, s)-nets in H. Niederreiter J. Spanier (ed) Monte Carlo and Quasi-Monte Carlo Methods 1998 2000 Springer Berlin 368-376
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998 , pp. 368-376
    • Martin, W.J.1
  • 33
    • 0038853614 scopus 로고    scopus 로고
    • A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets
    • W.J. Martin D.R. Stinson A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets Canad. Math. Bull. 42 1999 359-370
    • (1999) Canad. Math. Bull. , vol.42 , pp. 359-370
    • Martin, W.J.1    Stinson, D.R.2
  • 34
    • 0033468368 scopus 로고    scopus 로고
    • Association schemes for ordered orthogonal arrays and (t, m, s)-nets
    • W.J. Martin D.R. Stinson Association schemes for ordered orthogonal arrays and (t, m, s) -nets Canad. J. Math. 51 1999 326-346
    • (1999) Canad. J. Math. , vol.51 , pp. 326-346
    • Martin, W.J.1    Stinson, D.R.2
  • 35
    • 0000382131 scopus 로고    scopus 로고
    • 2-discrepancy for anchored boxes
    • 2 -discrepancy for anchored boxes J. Complexity 14 1998 527-556
    • (1998) J. Complexity , vol.14 , pp. 527-556
    • Matoušek, J.1
  • 37
    • 0040083404 scopus 로고    scopus 로고
    • Orthogonal hypercubes and related designs
    • G.L. Mullen Orthogonal hypercubes and related designs J. Statist. Planning Inference 73 1998 177-188
    • (1998) J. Statist. Planning Inference , vol.73 , pp. 177-188
    • Mullen, G.L.1
  • 38
    • 0002644222 scopus 로고
    • Tables of (t, m, s)-net and (t, s)-sequence parameters
    • H. Niederreiter, P.J.-S. Shiue (Eds.) Lecture Notes in Statistics Springer, New York
    • G.L. Mullen, A. Mahalanabis, H. Niederreiter, Tables of (t, m, s)-net and (t, s)-sequence parameters, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Lecture Notes in Statistics, vol. 106, Springer, New York, 1995, pp. 58-86.
    • (1995) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing , vol.106 , pp. 58-86
    • Mullen, G.L.1    Mahalanabis, A.2    Niederreiter, H.3
  • 39
    • 0007321817 scopus 로고
    • Low-discrepancy point sets
    • H. Niederreiter Low-discrepancy point sets Monatsh. Math. 102 1986 155-167
    • (1986) Monatsh. Math. , vol.102 , pp. 155-167
    • Niederreiter, H.1
  • 40
    • 8344289793 scopus 로고
    • Point sets and sequences with small discrepancy
    • H. Niederreiter Point sets and sequences with small discrepancy Monatsh. Math. 104 1987 273-337
    • (1987) Monatsh. Math. , vol.104 , pp. 273-337
    • Niederreiter, H.1
  • 41
    • 0002071152 scopus 로고
    • Low-discrepancy and low-dispersion sequences
    • H. Niederreiter Low-discrepancy and low-dispersion sequences J. Number Theory 30 1988 51-70
    • (1988) J. Number Theory , vol.30 , pp. 51-70
    • Niederreiter, H.1
  • 42
    • 8344236171 scopus 로고
    • A combinatorial problem for vector spaces over finite fields
    • H. Niederreiter A combinatorial problem for vector spaces over finite fields Discrete Math. 96 1991 221-228
    • (1991) Discrete Math. , vol.96 , pp. 221-228
    • Niederreiter, H.1
  • 43
    • 0000951059 scopus 로고
    • Low-discrepancy point sets obtained by digital constructions over finite fields
    • H. Niederreiter Low-discrepancy point sets obtained by digital constructions over finite fields Czechoslovak Math. J. 42 1992 143-166
    • (1992) Czechoslovak Math. J. , vol.42 , pp. 143-166
    • Niederreiter, H.1
  • 45
    • 0001940595 scopus 로고    scopus 로고
    • Constructions of (t, m, s) -nets
    • H. Niederreiter J. Spanier (eds) Springer Berlin
    • H. Niederreiter Constructions of (t, m, s)-nets in H. Niederreiter J. Spanier (eds) Monte Carlo and Quasi-Monte Carlo Methods 1998 2000 Springer Berlin 70-85
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998 , pp. 70-85
    • Niederreiter, H.1
  • 46
    • 0037438152 scopus 로고    scopus 로고
    • Error bounds for quasi-Monte Carlo integration with uniform point sets
    • H. Niederreiter Error bounds for quasi-Monte Carlo integration with uniform point sets J. Comput. Appl. Math. 150 2003 283-292
    • (2003) J. Comput. Appl. Math. , vol.150 , pp. 283-292
    • Niederreiter, H.1
  • 47
    • 0345492044 scopus 로고    scopus 로고
    • The existence of good extensible polynomial lattice rules
    • H. Niederreiter The existence of good extensible polynomial lattice rules Monatsh. Math. 139 2003 295-307
    • (2003) Monatsh. Math. , vol.139 , pp. 295-307
    • Niederreiter, H.1
  • 48
    • 0037716324 scopus 로고    scopus 로고
    • Some current issues in quasi-Monte Carlo methods
    • H. Niederreiter Some current issues in quasi-Monte Carlo methods J. Complexity 19 2003 428-433
    • (2003) J. Complexity , vol.19 , pp. 428-433
    • Niederreiter, H.1
  • 51
    • 0041832237 scopus 로고    scopus 로고
    • Constructions of digital nets using global function fields
    • H. Niederreiter F. Özbudak Constructions of digital nets using global function fields Acta Arith. 105 2002 279-302
    • (2002) Acta Arith. , vol.105 , pp. 279-302
    • Niederreiter, H.1    Özbudak, F.2
  • 52
    • 3142658005 scopus 로고    scopus 로고
    • Matrix-product constructions of digital nets
    • H. Niederreiter F. Özbudak Matrix-product constructions of digital nets Finite Fields Appl. 10 2004 464-479
    • (2004) Finite Fields Appl. , vol.10 , pp. 464-479
    • Niederreiter, H.1    Özbudak, F.2
  • 53
    • 0035649452 scopus 로고    scopus 로고
    • Duality for digital nets and its applications
    • H. Niederreiter G. Pirsic Duality for digital nets and its applications Acta Arith. 97 2001 173-182
    • (2001) Acta Arith. , vol.97 , pp. 173-182
    • Niederreiter, H.1    Pirsic, G.2
  • 54
    • 0035702599 scopus 로고    scopus 로고
    • The microstructure of (t,m,s)-nets
    • H. Niederreiter G. Pirsic The microstructure of (t, m, s)-nets J. Complexity 17 2001 683-696
    • (2001) J. Complexity , vol.17 , pp. 683-696
    • Niederreiter, H.1    Pirsic, G.2
  • 55
    • 0042118864 scopus 로고    scopus 로고
    • Kronecker product construction for digital nets
    • K.-T. Fang F.J. Hickernell H. Niederreiter (eds) Springer Berlin
    • H. Niederreiter G. Pirsic A Kronecker product construction for digital nets in K.-T. Fang F.J. Hickernell H. Niederreiter (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000 2002 Springer Berlin 396-405
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 396-405
    • Niederreiter, H.1    Pirsic, G.2
  • 56
    • 0000324792 scopus 로고    scopus 로고
    • Quasirandom points and global function fields
    • S. Cohen, H. Niederreiter (Eds.) London Mathematical Society Lecture Note Series Cambridge University Press, Cambridge
    • H. Niederreiter, C.P. Xing, Quasirandom points and global function fields, in: S. Cohen, H. Niederreiter (Eds.), Finite Fields and Applications, London Mathematical Society, Lecture Note Series, vol. 233, Cambridge University Press, Cambridge, 1996, pp. 269-296.
    • (1996) Finite Fields and Applications , vol.233 , pp. 269-296
    • Niederreiter, H.1    Xing, C.P.2
  • 57
    • 0001600529 scopus 로고    scopus 로고
    • Nets, (t, s)-sequences, and algebraic geometry
    • P. Hellekalek, G. Larcher (Eds.) Lecture Notes in Statistics Springer, New York
    • H. Niederreiter, C.P. Xing, Nets, (t, s)-sequences, and algebraic geometry, in: P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Lecture Notes in Statistics, vol. 138, Springer, New York, 1998, pp. 267-302.
    • (1998) Random and Quasi-Random Point Sets , vol.138 , pp. 267-302
    • Niederreiter, H.1    Xing, C.P.2
  • 58
    • 0003673377 scopus 로고    scopus 로고
    • Rational Points on Curves over Finite Fields: Theory and Applications
    • Cambridge: Cambridge University Press
    • H. Niederreiter C.P. Xing Rational Points on Curves over Finite Fields: Theory and Applications 2001 Cambridge University Press Cambridge
    • (2001)
    • Niederreiter, H.1    Xing, C.P.2
  • 59
    • 23044532627 scopus 로고    scopus 로고
    • Constructions of digital nets
    • H. Niederreiter C.P. Xing Constructions of digital nets Acta Arith. 102 2002 189-197
    • (2002) Acta Arith. , vol.102 , pp. 189-197
    • Niederreiter, H.1    Xing, C.P.2
  • 60
    • 0001491057 scopus 로고
    • Randomly permuted (t, m, s)-nets and (t, s)-sequences
    • H. Niederreiter, P.J.-S. Shiue (Eds.) Lecture Notes in Statistics Springer, New York
    • A.B. Owen, Randomly permuted (t, m, s)-nets and (t, s)-sequences, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Lecture Notes in Statistics, vol. 106, Springer, New York, 1995, pp. 299-317.
    • (1995) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing , vol.106 , pp. 299-317
    • Owen, A.B.1
  • 61
    • 0013036522 scopus 로고    scopus 로고
    • Monte Carlo variance of scrambled net quadrature
    • A.B. Owen Monte Carlo variance of scrambled net quadrature SIAM J. Numer. Anal. 34 1997 1884-1910
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1884-1910
    • Owen, A.B.1
  • 62
    • 0000828041 scopus 로고    scopus 로고
    • Scrambling Sobol' and Niederreiter-Xing points
    • A.B. Owen Scrambling Sobol' and Niederreiter-Xing points J. Complexity 14 1998 466-489
    • (1998) J. Complexity , vol.14 , pp. 466-489
    • Owen, A.B.1
  • 63
    • 4243059534 scopus 로고    scopus 로고
    • Variance with alternative scramblings of digital nets
    • A.B. Owen Variance with alternative scramblings of digital nets ACM Trans. Modeling Comp. Simulation 13 2003 363-378
    • (2003) ACM Trans. Modeling Comp. Simulation , vol.13 , pp. 363-378
    • Owen, A.B.1
  • 66
    • 2442707909 scopus 로고    scopus 로고
    • A software implementation of Niederreiter-Xing sequences
    • K.-T. Fang F.J. Hickernell H. Niederreiter (eds) Springer Berlin
    • G. Pirsic A software implementation of Niederreiter-Xing sequences in K.-T. Fang F.J. Hickernell H. Niederreiter (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000 2002 Springer Berlin 434-445
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 434-445
    • Pirsic, G.1
  • 67
    • 23044458357 scopus 로고    scopus 로고
    • Cyclic digital nets, hyperplane nets and multivariate integration in Sobolev spaces
    • preprint
    • G. Pirsic, J. Dick, F. Pillichshammer, Cyclic digital nets, hyperplane nets and multivariate integration in Sobolev spaces, preprint, 2005.
    • (2005)
    • Pirsic, G.1    Dick, J.2    Pillichshammer, F.3
  • 68
    • 0035704063 scopus 로고    scopus 로고
    • Calculation of the quality parameter of digital nets and application to their construction
    • G. Pirsic W.Ch. Schmid Calculation of the quality parameter of digital nets and application to their construction J. Complexity 17 2001 827-839
    • (2001) J. Complexity , vol.17 , pp. 827-839
    • Pirsic, G.1    Schmid, W.Ch.2
  • 70
    • 0000033796 scopus 로고    scopus 로고
    • Shift-nets: A new class of binary digital (t, m, s)-nets
    • H. Niederreiter, P. Hellekalek, G. Larcher, P. Zinterhof (Eds.) Lecture Notes in Statistics Springer, New York
    • W.Ch. Schmid, Shift-nets: A new class of binary digital (t, m, s)-nets, in: H. Niederreiter, P. Hellekalek, G. Larcher, P. Zinterhof (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics, vol. 127, Springer, New York, 1998, pp. 369-381.
    • (1998) Monte Carlo and Quasi-Monte Carlo Methods 1996 , vol.127 , pp. 369-381
    • Schmid, W.Ch.1
  • 71
    • 0001152675 scopus 로고    scopus 로고
    • The exact quality parameter of nets derived from Sobol' and Niederreiter sequences
    • O.P. Iliev et al. (eds) World Scientific Singapore
    • W.Ch. Schmid The exact quality parameter of nets derived from Sobol' and Niederreiter sequences in O.P. Iliev et al. (eds) Recent Advances in Numerical Methods and Applications II 1999 World Scientific Singapore 296-304
    • (1999) Recent Advances in Numerical Methods and Applications II , pp. 296-304
    • Schmid, W.Ch.1
  • 72
    • 0003220082 scopus 로고    scopus 로고
    • Improvements and extensions of the "Salzburg tables" by using irreducible polynomials
    • H. Niederreiter J. Spanier (eds) Springer Berlin
    • W.Ch. Schmid Improvements and extensions of the "Salzburg tables"; by using irreducible polynomials in H. Niederreiter J. Spanier (eds) Monte Carlo and Quasi-Monte Carlo Methods 1998 2000 Springer Berlin 436-447
    • (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998 , pp. 436-447
    • Schmid, W.Ch.1
  • 73
    • 0034919244 scopus 로고    scopus 로고
    • Projections of digital nets and sequences
    • W.Ch. Schmid Projections of digital nets and sequences Math. Comp. Simulation 55 2001 239-247
    • (2001) Math. Comp. Simulation , vol.55 , pp. 239-247
    • Schmid, W.Ch.1
  • 74
    • 33846262009 scopus 로고    scopus 로고
    • MinT: A database for optimal net parameters
    • preprint
    • R. Schürer, W.Ch. Schmid, MinT: A database for optimal net parameters, preprint, 2004.
    • (2004)
    • Schürer, R.1    Schmid, W.Ch.2
  • 75
    • 0043120784 scopus 로고    scopus 로고
    • Coding theory and uniform distributions (Russian)
    • M.M. Skriganov Coding theory and uniform distributions (Russian) Algebra Anal. 13 2001 191-239
    • (2001) Algebra Anal. , vol.13 , pp. 191-239
    • Skriganov, M.M.1
  • 76
    • 23044450662 scopus 로고    scopus 로고
    • Polynomial arithmetic analogue of Hickernell sequences
    • Springer Berlin
    • S. Tezuka Polynomial arithmetic analogue of Hickernell sequences H. Niederreiter Monte Carlo and Quasi-Monte Carlo Methods 2002 2004 Springer Berlin 451-459
    • (2004) Monte Carlo and Quasi-Monte Carlo Methods 2002 , pp. 451-459
    • Tezuka, S.1
  • 77
    • 0348233983 scopus 로고    scopus 로고
    • I-binomial scrambling of digital nets and sequences
    • S. Tezuka H. Faure I -binomial scrambling of digital nets and sequences J. Complexity 19 2003 744-757
    • (2003) J. Complexity , vol.19 , pp. 744-757
    • Tezuka, S.1    Faure, H.2
  • 79
    • 0036222370 scopus 로고    scopus 로고
    • The discrepancy and gain coefficients of scrambled digital nets
    • R.-X. Yue F.J. Hickernell The discrepancy and gain coefficients of scrambled digital nets J. Complexity 18 2002 135-151
    • (2002) J. Complexity , vol.18 , pp. 135-151
    • Yue, R.-X.1    Hickernell, F.J.2
  • 80
    • 0042859915 scopus 로고    scopus 로고
    • On the asymptotic distribution of scrambled net quadrature
    • W.-L. Loh On the asymptotic distribution of scrambled net quadrature Ann. Statist. 31 2003 1282-1324
    • (2003) Ann. Statist. , vol.31 , pp. 1282-1324
    • Loh, W.-L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.