lgruen / diag0m2

(t, m, s)-Nets and Maximized Minimum Distance, Part II

with A. Keller.

In P. L'Ecuyer and A. Owen (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer-Verlag, Berlin, 2009.

Abstract: The quality parameter t of (t,m,s)-nets controls extensive stratification properties of the generated sample points. However, the definition allows for points that are arbitrarily close across strata boundaries. We continue the investigation of (t,m,s)-nets under the constraint of maximizing the mutual distance of the points on the unit torus and present two new constructions along with algorithms. The first approach is based on the fact that reordering (t,s)-sequences can result in (t,m,s+1)-nets with varying toroidal distance, while the second algorithm generates points by permutations instead of matrices.

Paper