Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [5–7]. For the special case of extensible Korobov sequences, parameters can be found in [6]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [6]. Key words: lattice sequences, Korobov rules, highly-uniform point sets 2000 MSC: 11D45, 11K36, 65C05, 65D30

• Type: Journal
• Year: 2007
• Where: JC
• Authors: Hardeep S. Gill, Christiane Lemieux
• Keywords: Extensible Lattice Sequences, JC 2007, Parameters, Sequences