Reduced Digital Nets

In the recent papers “The fast reduced QMC matrix-vector product” (Dick, Ebert, Herrmann, Kritzer, Longo; J. Comput. Appl. Math., 2024) and “Column reduced digital nets” (Anupindi, Kritzer; Numer. Algorithms, 2025), it was proposed to use QMC rules based on reduced digital nets which provide a speed-up in the computation of QMC vector-matrix products that may occur in practical applications. In this paper, we provide upper bounds on the quality parameter of row reduced and column-row reduced digital nets, which are helpful for the error analysis of using reduced point sets as integration nodes in a QMC rule. We also give remarks on further aspects and comparisons of row reduced, column reduced, and column-row reduced digital nets.