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Nets, (t, s)-Sequences, and Codes

  • Conference paper
Monte Carlo and Quasi-Monte Carlo Methods 2006

Summary

Nets and (t, s)-sequences are standard sources of quasirandom points for quasi-Monte Carlo methods. Connections between nets and error-correcting codes have been noticed for a long time, and these links have become even more pronounced with the development of the duality theory for digital nets. In this paper, we further explore these fascinating connections. We present also a recent construction of digital (t, s)-sequences using global function fields and new general constructions of nets and (t, s)-sequences.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

Authors
  1. Harald Niederreiter
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ulm University, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Alexander Keller

  2. Department of Computer Science, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Stefan Heinrich

  3. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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Niederreiter, H. (2008). Nets, (t, s)-Sequences, and Codes. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_5

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