Sets in ${\mathbb{R}}^d$ with slow-decaying density that avoid an unbounded collection of distances

Alex Rice

For any $d\in \mathbb{N}$ and any function $f:(0,\infty )\to [0,1]$ with $f(R)\to 0$ as $R\to \infty$, we construct a set $A\subseteq {\mathbb{R}}^d$ and a sequence $R_n\to \infty$…