2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138216This paper is a companion to our prior paper arXiv:0705.4619 on the `Small Ball Inequality in All Dimensions.' In it, we address a more restrictive inequality, and obtain a non-trivial, explicit bound, using a single essential estimate from our prior paper. The prior bound was not explicit and much more involved.10 pagesClassical Analysis and ODEs42A05 (Primary); 41A46, 11K38, 42A55 (Secondary)text