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Peter Kritzer
On some remarkable properties of the two-dimensional Hammersley point set in base 2
Journal de théorie des nombres de Bordeaux, 18 no. 1 (2006), p. 203-221, doi: 10.5802/jtnb.540
Article PDF | Reviews MR 2245882 | Zbl 1103.11024

Résumé - Abstract

We study a special class of $(0,m,2)$-nets in base 2. In particular, we are concerned with the two-dimensional Hammersley net that plays a special role among these since we prove that it is the worst distributed with respect to the star discrepancy. By showing this, we also improve an existing upper bound for the star discrepancy of digital $(0,m,2)$-nets over $\mathbb{Z}_{2}$. Moreover, we show that nets with very low star discrepancy can be obtained by transforming the Hammersley point set in a suitable way.

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