A new upper bound for the size of $s$-distance sets in boxes

Gábor Hegedüs

Let $q,d\ge 2$ be integers. Define $$J(q,d):=\frac{1}{q}\left(\underset{0<x<1}{\min }\frac{1-x^q}{1-x}{x}^{-\frac{q-1}{d}}\right).$$ Let $\mbox{$\cal G$}\subseteq {\mathbb R}^n$ be an arbitrar…