Point sets with low lp-discrepancy

Mathematica Slovaca

Volumn 57, Issue 1, 2007, Pages 11-32

  Kritzer, Peter ^a   Pillichshammer, Friedrich ^b  

^a UNIVERSITY OF SALZBURG   (Austria)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349960012     PISSN: 01399918     EISSN: 13372211     Source Type: Journal    
DOI: 10.2478/s12175-007-0011-x     Document Type: Article

References (17)

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4. DRMOTA, M. — TICHY, R.F.: Sequences. Discrepancies and Applications. Lecture Notes in Math. 1651, Springer-Verlag, Berlin, 1997.
5. ENTACHER, K.: Haar function based estimates of the star-discrepancy of plane digital nets Monatsh. Math. 130 (2000), 99-108.
6. HALTON, J.H. — ZAREMBA, S.K.: The extreme and the L2 discrepancies of some plane sets Monatsh. Math. 73 (1969), 316-328.
7. KRITZER, P.: On some remarkable properties of the two-dimensional Hammersley point set in base 2 J. Theor. Nombres Bordeaux 18 (2006). 203-221.
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10. LARCHER, G. — PILLICHSHAMMER, F.: Sums of distances to the nearest integer and the discrepancy of digital nets Acta Arith. 106 (2003), 379-408.
11. MATOUSEK, J.: Geometric Discrepancy. Algorithms Combin. 18 Springer, Berlin, 1999.
12. NIEDERREITER, H.: Point sets and sequences with small discrepancy Monatsh. Math. 104 (1987), 273-337.
13. NIEDERREITER, H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, 1992.
14. PILLICHSHAMMER, F.: On the Lp-discrepancy of the Hammersley Point Set Monatsh. Math. 136 (2002), 67-79.
15. ROTH, K.F.: On irregularities of distribution Mathematika 1 (1954), 73-79.
16. SCHMIDT, W.M.: Irregularities of distribution X. In: Number Theory and Algebra Academic Press, New York, 1977, pp. 311-329.
17. VILENKIN, I.V.: Plane nets of Integration Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 189-196 [English translation in: Comput. Math. Math. Phys. 7 (1967), 258-267.]