3 problems

For a sequence of positive distances $(r_j)_{j\geq 1}$, let $\mathbf{m}_{\mathbb{R}^2}((r_j)_{j\geq 1})$ denote the supremum of the upper densities of sets in $\mathbb{R}^2$ avoidi…

Let $K\subset[1,\infty)$ be a compact set with $1\in K$. A sphere packing is $K$-admissible if all distances between distinct centers avoid $K$ in the paper's normalization, and a…

Let $\Lambda\subset\mathbb{R}^d$ be an even unimodular lattice with minimal norm $\sqrt{a}$, where $a$ is an even integer. A sphere packing is admissible for a set of normalized di…