Explicit construction of normal lattice configurations
Volume 102 / 2005
Colloquium Mathematicum 102 (2005), 33-47
MSC: Primary 11K16, 28D.
DOI: 10.4064/cm102-1-4
Abstract
We extend Champernowne's construction of normal numbers to base $b$ to the ${\mathbb Z}^d$ case and obtain an explicit construction of a generic point of the ${\mathbb Z}^d$ shift transformation of the set $\{ 0,1,\ldots,b-1 \}^{{\mathbb Z}^d}$.
