The Algebraic-Geometry Approach to Low-Discrepancy Sequences
We give a survey of recent work of the authors in which low-discrepancy sequences are constructed by new methods based on algebraic geometry. The most powerful of these methods employ algebraic curves over finite fields with many rational points. These methods yield significant improvements on all earlier constructions. In fact, we obtain (t, s)sequences in an arbitrary base b where for fixed b the quality parameter t has the least possible order of magnitude when considered as a function of the dimension s., namely t grows linearly in s.
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