Given a polyhedron
$$Ax\leq b$$
where we assume $A\in\mathbb Q^{m\times n}$ and $b\in\mathbb Q^{m}$ and it takes $L$ bits to represent the inequalities what is a good bound on the quantity $\|y\|_\infty$ where $y$ is in the set $\{x\in\mathbb Z^n:Ax\leq b\}$ holds? Under what conditions it depends only on $n$?
