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. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.
翻译:我们展示了LatNet 构建器, 这是一种软件工具, 用来寻找在基底2中, 准蒙卡罗(QMC) 和随机准蒙卡罗(RQMC) 抽样对美元元元单位超立方体进行抽样的优劣参数。 选择标准是给不同的坐标子集带来不同权重的优劣数字。 它们是最坏的错误( QMC) 或差异( RQMC) 的上限, 对于重新排列的原格子体来说, 在某些Hilbert 功能空间中最多有一个标准。 我们总结了Hilbert 空间、 差异、 重量类型、 功绩、 建筑类型 和LatNet 构建器所支持的搜索方法。 我们简要讨论其组织, 我们简单描述它能做什么 。