A construction of (t, s)-sequences with finite-row generating matrices using global function fields

For any prime power q and any dimension s >= 1, we present a construction of (t, s)-sequences in base q with finite-row generating matrices such that, for fixed q, the quality parameter t is asymptotically optimal as a function of s as s -> infinity. This is the first construction of (t, s)-sequences that yields finite-row generating matrices and asymptotically optimal quality parameters at the same time. The construction is based on global function fields. We put the construction into the framework of (u, e, s)-sequences that was recently introduced by Tezuka. In this way we obtain in many cases better discrepancy bounds for the constructed sequences than by previous methods for bounding the discrepancy. (C) 2012 Elsevier Inc. All rights reserved.