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Low-discrepancy point sets. (English) Zbl 0584.10034

Various point sets in the s-dimensional unit cube with small discrepancy are constructed. One construction principle is based on the method of good lattice points. Another construction principle employs schemes for setting up the digit expansions (relative to a given base) of the coordinates of the points. These schemes use linear recurrence relations in finite fields or linear functionals from an extension field to a finite ground field. The bounds for the discrepancy are obtained by a new method of estimating the discrepancy in terms of exponential sums that was developed recently by the author [Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. (to appear)].

MSC:

11K38 Irregularities of distribution, discrepancy
11K06 General theory of distribution modulo \(1\)
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References:

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