Johnson optimality and uniqueness for distance ratio $1:\sqrt{2}$

Bryan Bu, Chin-Yen Lee, Yu-Hang Sheng +3

We prove that a two-distance set in ${\mathbb{R}}^d$ with distance ratio $1:\sqrt{2}$ has at most $d(d+1)/2$ points for every $d\ge 9$. Equality in full affine dimension characterizes…