The construction of good extensible Korobov rules
Given the point set \(P_s=\{h\vec z/n +\Delta: h=1,\dots,n-1\} \subset [0,1)^s\), where \(z=(1,a,\dots,a^{s_i-1})\) for some \(a\in \{1,2,\ldots, n-1\}\) and \(\Delta \in [0,1)^s\) is chosen i.i.d. the authors want to find \(a\) such that the worst case error for QMC-integration is small. As the authors point out, for applications it is important to find lattice rules that give small QMC-integration errors simultaneously in several dimensions \(\mathcal S=\{s_1,\dots, s_d\}\). In this sense the algorithm given in the paper finds good \(a\)'s. In the last section the authors give also numerical examples to confirm their algorithm.
scientific article; zbMATH DE number 5138269
scientific article