Chirotopes of Random Points in Space are Realizable on a Small Integer Grid

Jean Cardinal, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano

We prove that with high probability, a uniform sample of $n$ points in a convex domain in ${\mathbb{R}}^d$ can be rounded to points on a grid of step size proportional to $1/n^{d+1+ε…