Dot products in ${\mathbb{F}}_q^3$ and the Vapnik-Chervonenkis dimension

A. Iosevich, B. McDonald, M. Sun

Given a set $E\subset {\mathbb{F}}_q^3$, where ${\mathbb{F}}_q$ is the field with $q$ elements. Consider a set of "classifiers" ${\mathcal{H}}_t^3(E)=\{h_y:y\in E\}$, where $h_y(x)=1$ if…