文摘
For any prime power q and any dimension , we present a construction of -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 . This is the first construction of -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 -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.