The exponent of discrepancy is at least 1.0669

Journal of Complexity

Volumn 14, Issue 4, 1998, Pages 448-453

  Matoušek, Jiří ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038624683     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1998.0485     Document Type: Article

References (16)

1. Beck J., Chen W. Irregularities of Distribution. 1987;Cambridge Univ. Press, Cambridge.
2. Beck J., Sós. Discrepancy theory. Handbook of Combinatorics. 1995;North-Holland, Amsterdam. p. 1405-1446.
3. Chen W. L. On irregularities of distribution II. Quart. J. Math. Oxford Ser. (2). 34:1983;257-279.
4. Drmota M., Tichy R. F. Sequences, Discrepancies and Applications. Lecture Notes in Mathematics. 1651:1997;Springer-Verlag, New York/Berlin.
5. p-metric, 2≤p. Dokl. Akad. Nauk SSSR. 252:1980;805-807.
6. 2. Math. Comput. 65:1996;1621-1633.
7. Hickernell F. J. The mean square discrepancy of randomized nets. ACM Trans. Modeling Comput. Simul. 6:1996;274-296.
8. Kuipers L, Niederreiter H. Uniform Distribution of Sequences. 1974;Wiley, New York.
9. 2. J. Complexity. 14:1998;417-453.
10. Niederreiter H. Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Applied Mathematics. 63:1992;SIAM, Philadelphia.
11. Roth K. F. On irregularities of distribution. Mathematika. 1:1954;73-79.
12. Roth K. F. On irregularities of distribution IV. Acta Arith. 37:1980;67-75.
13. Skriganov M. M. Constructions of uniform distributions in terms of geometry of numbers. Algebra i Anal. 6:1994;200-223.
14. Warnock T. T. Computational investigations of low-discrepancy point sets. Applications of Number Theory to Numerical Analysis. 1972;Academic Press, New York. p. 319-343.
15. Wasilkowski G. W., Woźniakowski H. The exponent of discrepancy is at most 1.4778... Math. Comput. 1997;1125-1132.
16. Woźniakowski H. Average case complexity of multivariate integration. Bull. Amer. Math. Soc. 24:1991;185-194.