On some remarkable properties of the two-dimensional Hammersley point set in base 2

DOI10.5802/jtnb.540zbMath1103.11024OpenAlexW1984300770MaRDI QIDQ2433586

Peter Kritzer

Publication date: 2 November 2006

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2006__18_1_203_0

zbMATH Keywords

Hammersley point setstar discrepancy2)\)-netsdigital \((0digital shiftsm

Mathematics Subject Classification ID

Irregularities of distribution, discrepancy (11K38) Special sequences (11K31)

Related Items (8)

\(L_p\) discrepancy of generalized two-dimensional Hammersley point sets ⋮ From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules ⋮ Finding exact formulas for the $L_2$ discrepancy of digital $(0,n,2)$-nets via Haar functions ⋮ Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces ⋮ Improved upper bounds on the star discrepancy of \((t,m,s)\)-nets and \((t,s)\)-sequences ⋮ A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets ⋮ A best possible upper bound on the star discrepancy of (t, m, 2)-nets ⋮ Point sets with low L p-discrepancy

Cites Work

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• Sequences, discrepancies and applications
• A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley
• On the star-discrepancy of generalized Hammersley sequences in two dimensions
• Star discrepancy estimates for digital \((t,m,2)\)-nets and digital \((t,2)\)-sequences over \(\mathbb Z_2\)
• The extreme and \(L^2\) discrepancies of some plane sets
• Sums of distances to the nearest integer and the discrepancy of digital nets
• Matrix theory. Basic results and techniques

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