Randomly piercing algebraic sets

Daniel Altman, Nathan Tung

We show, for example, that if one samples \[\frac{\log p}{2\log(1+(p-1)^{-1})} \cdot n^2(1 + o_{n\to \infty}(1))\] points in ${\mathbb{F}}_p^n$ at random then asymptotically almost s…