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Irregularities of distribution of digital \(0,1\)-sequences in prime base. (English) Zbl 1084.11041

The author compares digital \((0,1)\)-sequences generated by nonsingular upper triangular matrices in arbitrary prime bases to van der Corput sequences and shows these last ones are the worst distributed with respect to the star discrepancy, the extreme discrepancy, the \(L_2\)-discrepancy and the diaphony. Moreover, he obtains digital \((0,1)\)-sequences in arbitrary prime bases with good extreme discrepancy, quite comparable to the best generalized van der Corput sequences already found in preceding studies. See also earlier proofs of the author [Bull. Soc. Math. France 109, 143–182 (1981; Zbl 0488.10052), J. Number Th. 42, 47–56 (1992; Zbl 0768.11026), Acta Arith. 117, 125–148 (2005; Zbl 1080.11054)].

MSC:

11K38 Irregularities of distribution, discrepancy
11K45 Pseudo-random numbers; Monte Carlo methods
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