  Digital nets provide an efficient way to generate integration nodes of
quasi-Monte Carlo (QMC) rules. For certain applications, as e.g. in Uncertainty
Quantification, we are interested in obtaining a speed-up in computing products
of a matrix with the vectors corresponding to the nodes of a QMC rule. In the
recent paper "The fast reduced QMC matrix-vector product" (J. Comput. Appl.
Math. 440, 115642, 2024), a speed up was obtained by using so-called reduced
lattices and row reduced digital nets. In this work, we propose a different
multiplication algorithm where we exploit the repetitive structure of column
reduced digital nets instead of row reduced digital nets. This method has
advantages over the previous one, as it facilitates the error analysis when
using the integration nodes in a QMC rule. We also provide an upper bound for
the quality parameter of column reduced digital nets, and numerical tests to
illustrate the efficiency of the new algorithm.
