On some remarkable properties of the two-dimensional Hammersley point set in base 2
- [1] Department of Mathematics University of Salzburg Hellbrunnerstr. 34 A-5020 Salzburg, Austria
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 1, page 203-221
- ISSN: 1246-7405
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top- L. De Clerck, A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley. Monatsh. Math. 101 (1986), 261–278. Zbl0588.10059MR851948
- J. Dick, P. Kritzer, Star-discrepancy estimates for digital -nets and -sequences over . Acta Math. Hungar. 109 (3) (2005), 239–254. Zbl1102.11036MR2187287
- M. Drmota, R. F. Tichy, Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651, Springer, Berlin, 1997. Zbl0877.11043MR1470456
- H. Faure, On the star-discrepancy of generalized Hammersley sequences in two dimensions. Monatsh. Math. 101 (1986), 291–300. Zbl0588.10060MR851950
- J. H. Halton, S. K. Zaremba, The extreme and the discrepancies of some plane sets. Monatsh. Math. 73 (1969), 316–328. Zbl0183.31401MR252329
- L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences. John Wiley, New York, 1974. Zbl0281.10001MR419394
- G. Larcher, F. Pillichshammer, Sums of distances to the nearest integer and the discrepancy of digital nets. Acta Arith. 106 (2003), 379–408. Zbl1054.11039MR1957912
- H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. CBMS–NSF Series in Applied Mathematics 63, SIAM, Philadelphia, 1992. Zbl0761.65002MR1172997
- F. Zhang, Matrix Theory. Springer, New York, 1999. Zbl0948.15001MR1691203