Article
Note on the Extreme Discrepancy of the Hammersley Net in Base 2
Authors
Abstract
In this note, we study lower bounds on the extreme discrepancy of the Hammersley net in base 2. The Hammersley net in base 2 can be interpreted as a finite two-dimensional analogue of the well known (one-dimensional) van der Corput sequence in base 2. For the van der Corput sequence it is known that its star discrepancy equals its extreme discrepancy. In this paper, we prove the rather surprising fact that the same does not hold for the Hammersley net, by giving lower bounds on its extreme discrepancy. We furthermore state a few remarks on upper bounds and conclude with a conjecture.
Keywords
Extreme discrepancy, star discrepancy, Hammersley net, van der Corput sequence, distance to the nearest integer.
Citation
Kritzer, P. (2011). Note on the extreme discrepancy of the hammersley net in base 2. Uniform Distribution Theory, 6(1), 9–19.
P. Kritzer, “Note on the extreme discrepancy of the hammersley net in base 2,” Uniform Distribution Theory, vol. 6, no. 1, pp. 9–19, 2011.
Kritzer P. Note on the extreme discrepancy of the hammersley net in base 2. Uniform Distribution Theory. 2011;6(1):9–19.
Kritzer, P. (2011), ‘Note on the extreme discrepancy of the hammersley net in base 2’, Uniform Distribution Theory, 6(1), pp. 9–19.
Kritzer, Peter. “Note on the Extreme Discrepancy of the Hammersley Net in Base 2.” Uniform Distribution Theory, vol. 6, no. 1, 2011, pp. 9–19.
Kritzer, Peter. “Note on the Extreme Discrepancy of the Hammersley Net in Base 2.” Uniform Distribution Theory 6, no. 1 (2011): 9–19.
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Published by: Engineering Journals
