Halton-type sequences from global function fields

For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.