Parameterization of Zinterhof Sequences for GRID-based QMC Integration

We have already investigated blocked and leaped substreams of the Zinterhof sequence for the use in the GRID. When comparing this sequence to others they have either the drawback of being computationally expensive (e.g. Niederreiter/Xing sequence) or have some kind of problematic defect (e.g. Sobol’ sequence). In contrast, the Zinterhof sequence behaves well and is computationally inexpensive. In this paper we will demonstrate the use of parameterized Zinterhof sequences, where each processing element uses a different point generating sequence. In this context, the Zinterhof sequence is used on all processing elements but with a shift in dimension to generate low correlated sequences. Additionally the benefits of using parameterization in the GRID are discussed.