What is the maximum number of integer points $\#M$ in a dimension $n$ closed bounded convex polytope $M$ given by $Ax\leq b$ with number $m$ of constraints and $O(d)$ bits in any entry of $A\in\Bbb Z^{m\times n}$ and $b\in\Bbb Z^m$? Can $\#M$ be $2^{2^{\omega(d)}}$ lattice points?