Groupe d’études et de recherche en analyse des décisions

# A tool for custom construction of QMC and RQMC point sets

## Pierre L'Ecuyer, Pierre Marion, Maxime Godin et Florian Puchhammer

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the $$s$$-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. Various Hilbert spaces, figures of merit, types of constructions, and search methods are covered by the tool. We provide simple illustrations of what it can do.

, 16 pages