A non-lattice periodic point set beating the optimal lattice packing-covering constant in dimension five

Sven Ahrend, Mathieu Dutour Sikirić

The packing-covering constant of a point set $X\subseteq {\mathbb{R}}^d$ is $\gamma (X)=\mu (X)/\rho (X)$, the covering radius divided by the packing radius. Among lattices, its minimum ${\gamma }_d$ is k…