Sums of distances to the nearest integer and the discrepancy of digital nets

Acta Arithmetica

Volumn 106, Issue 4, 2003, Pages 379-408

  Larcher, G ^a   Pillichshammer, F ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Digital nets; Discrepancy; Distance to the nearest integer; Walsh series analysis

Indexed keywords

EID: 0041831009     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa106-4-4     Document Type: Article

References (8)

1. R. Béjian, Minoration de la discrépance d'une suite quelconque sur T, Acta Arith. 41 (1982), 185-202.
2. 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.
3. K. Entacher, Haar function based estimates of the star-discrepancy of plane digital nets, ibid. 130 (2000), 99-108.
4. 2 discrepancies of some plane sets, ibid. 73 (1969), 316-328.
5. G. Larcher, H. Niederreiter and W. Ch. Schmid, Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration, ibid. 121 (1996), 231-253.
6. 2-discrepancy of symmetrized point sets, ibid. 132 (2001), 1-18.
7. G. Larcher and G. Pirsic, Base change problems for generalized Walsh series and multivariate numerical integration, Pacific J. Math. 189 (1999), 75-105.
8. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.