Metrical lower bounds on the discrepancy of digital Kronecker-sequences

Digital Kronecker-sequences are a non-archimedean analog of classical Kronecker-sequences whose construction is based on Laurent series over a finite field. In this paper it is shown that for almost all digital Kronecker-sequences the star discrepancy satisfies D-N* >= c(q, s)(log N)(s) log log N for infinitely many N is an element of N, where c(q, a) > 0 only depends on the dimension s and on the order q of the underlying finite field, but not on N. This result shows that a corresponding metrical upper bound due to Larcher is up to some log log N term best possible. (C) 2013 Elsevier Inc. All rights reserved.