Lattice tilings of Z^n by error balls B(n,2,3,0) exist only for n=3, none exist for B(n,2,k,k-1), and for k1>k2 with k1+k2+1 composite no tiling exists in sufficiently high dimension.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CO 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
On lattice tilings of $\mathbb{Z}^n$ by limited magnitude error balls $\mathcal{B}(n,2,k_{1},k_{2})$ with $k_1>k_2$
Lattice tilings of Z^n by error balls B(n,2,3,0) exist only for n=3, none exist for B(n,2,k,k-1), and for k1>k2 with k1+k2+1 composite no tiling exists in sufficiently high dimension.