This is an announcement for the paper “Dimension dependence of factorization problems: Hardy spaces and $SL_n^{\infty}$” by Richard Lechner<https://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1>. Abstract: Given $1\leq p<\infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $SL_n^{\infty}$”. We prove the following quantitative result: The identity operator on $W_n$ factors through any operator $T: W_N\rightarrow W_N$ which has large diagonal with respect to the Haar system, where $N$ depends \emph{linearly} on $n$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.02857