Low-discrepancy Sequence - The Best-known Sequences

The Best-known Sequences

Constructions of sequences are known such that

$D_{N}^{*}(x_1,\ldots,x_N)\leq C\frac{(\ln N)^{s}}{N}.$

where C is a certain constant, depending on the sequence. After Conjecture 2, these sequences are believed to have the best possible order of convergence. See also: van der Corput sequence, Halton sequences, Sobol sequences.

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