Constructions of Low-discrepancy Sequences - The Hammersley Set

The Hammersley Set

Let b1,...,bs-1 be coprime positive integers greater than 1. For given s and N, the s-dimensional Hammersley set of size N is defined by

x(n)=(g_{b_1}(n),\dots,g_{b_{s-1}}(n),\frac{n}{N})

for n = 1, ..., N. Then

D^*_N(x(1),\dots,x(N))\leq C\frac{(\log N)^{s-1}}{N}

where C is a constant depending only on b1, ..., bs−1.

Read more about this topic:  Constructions Of Low-discrepancy Sequences

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