2 problems

Let $\Gamma_n$ denote the graph considered in the paper, and let an isolated $n$-PTMC mean an isolated perfect total-multipacking code with parameter $n$. Existence conjecture. The…

Let $\Lambda_n=\mathbb{Z}^n$ and let a lattice $t$-PTMC be a lattice perfect total-multipacking code with parameter $t$. Nonexistence conjecture. There is no lattice $t$-PTMC in…