## On the Discrepancy of the $Î²$-Adic van der Corput Sequence

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 2, Page 345--366.

Ninomiya, Syoiti
On the Discrepancy of the $Î²$-Adic van der Corput Sequence
The $Î²$-adic \mbox{van der Corput} sequence is constructed. When $Î²$ satisfies some conditions, the order of discrepancy of the sequence become $O(\log M/M)$ or $O((\log M)^2/M)$.
Keywords: $Î²$-adic transformation, ergodic theory, low-discrepancy sequence, numerical integration, quasi-Monte Carlo method