The star discrepancy
In 2001 it has been shown by Heinrich, Novak, Wasilkowski and Woźniakowski that for every integer N ≥ 2there exist point sets 𝒫 in [0, 1)d with |𝒫| = N and
Unfortunately the result by Heinrich et al. and also later variants thereof by other authors are pure existence results and until now no explicit construction of point sets with the above properties is known. Quite recently Löbbe studied lacunary subsequences of Kronecker’s (n
α)-sequence and showed a metrical discrepancy bound of the form
In this paper we show a corresponding result for digital Kronecker sequences, which are a non-archimedean analog of classical Kronecker sequences.