Van der Corput sequence

A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base-n representation of the sequence of natural numbers (1, 2, 3, …).

The ${\displaystyle b}$-ary representation of the positive integer ${\displaystyle n\geq 1}$ is $${\displaystyle n~=~\sum _{k=0}^{L-1}d_{k}(n)b^{k}~=~d_{0}(n)b^{0}+\cdots +d_{L-1}(n)b^{L-1},}$$ where ${\displaystyle b}$ is the base in which the number ${\displaystyle n}$ is represented, and ${\displaystyle 0\leq d_{k}(n)<b;}$ that is, the ${\displaystyle k}$-th digit in the ${\displaystyle b}$-ary expansion of ${\displaystyle n.}$ The ${\displaystyle n}$-th number in the van der Corput sequence is $${\displaystyle g_{b}(n)~=~\sum _{k=0}^{L-1}d_{k}(n)b^{-k-1}~=~d_{0}(n)b^{-1}+\cdots +d_{L-1}(n)b^{-L}.}$$