  Since 1989, the best known lower bound on static data structures was Siegel's
classical cell sampling lower bound. Siegel showed an explicit problem with $n$
inputs and $m$ possible queries such that every data structure that answers
queries by probing $t$ memory cells requires space
$s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/t}\right)$. In this work,
we improve this bound for non-adaptive data structures to
$s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/(t-1)}\right)$ for all $t
\geq 2$.
  For $t=2$, we give a lower bound of $s>m-o(m)$, improving on the bound
$s>m/2$ recently proved by Viola over $\mathbb{F}_2$ and Siegel's bound
$s\geq\widetilde{\Omega}(\sqrt{mn})$ over other finite fields.
