Peter Kritzer, Gunther Leobacher, Friedrich Pillichshammer,
"Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets"
, in Josef Dick, Frances Y. Kuo, Gareth W. Peters, and Ian H. Sloan: Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer, Seite(n) 501--515, 2013
Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets
Sprache des Titels:
Monte Carlo and Quasi-Monte Carlo Methods 2012
In a series of recent articles point sets mixed from integration node sets in different sorts of quasi-Monte Carlo rules have been studied. In particular, a finite version, based on Hammersley and lattice point sets, was introduced by Kritzer, where the existence of such hybrid
point sets with low star discrepancy was shown. However, up to now it has
remained an open problem whether such low discrepancy hybrid point sets
can be explicitly constructed. In this paper, we solve this problem and discuss component-by-component constructions of the desired point sets.