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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?

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  • $\begingroup$ That seems way too big to me, but it's very possible I'm missing something. Should the bound of $2^{\omega(d)}$ be obvious to me? $\endgroup$ Apr 9, 2018 at 14:33

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