Let $A\in\left\{ 0,1\right\} ^{M\times N}$, where each row of $A$ has at most $d$ components equal to $1$, and $d\leq M\ll N\ll Md$.
Question: $\forall n\leq N$, what is $m\left(n\right)$, the maximal number of rows for which, $\forall A$, there exists a $m\left(n\right)\times n$ submatrix of $A$ which contains only $0$s?
