We give a lower bound on the Walsh figure of merit (WAFOM), which estimates the integration error for quasi-Monte Carlo (QMC) integration by a point set called a digital net. The logarithm of this lower bound is optimal up to a constant multiple, because the existence of point sets attaining the order was proved in K. Suzuki, "An explicit construction of point sets with large minimum Dick weight," to appear in J. Complexity.
"A lower bound on WAFOM." Hiroshima Math. J. 44 (3) 261 - 266, November 2014. https://doi.org/10.32917/hmj/1419619746