## On the $$L_p$$-discrepancy of the Hammersley point set.(English)Zbl 1010.11043

For the Hammersley point set $$\mathcal H_s$$ in base 2 in the unit square the $$L_p$$-discrepancy is computed as $\frac 1N \left(\frac {s^p}{2^{3p}}+O(s^{p-1})\right)^{1/p}$ for integers $$p$$, where $$N=2^s$$ is the number of points in $$\mathcal H_s$$. For $$p=1,2$$ the exact value is obtained. For $$p=2$$ this is a new proof of a result previously established by J. H. Halton and S. C. Zaremba [Monatsh. Math. 73, 316-328 (1969; Zbl 0183.31401)].

### MSC:

 11K38 Irregularities of distribution, discrepancy

### Keywords:

Hammersley point set; $$L_p$$-discrepancy

Zbl 0183.31401
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