There is no lattice tiling of Z^n by Lee spheres of radius 2 for n≥ 3
share
We prove the nonexistence of lattice tilings of Z^n by Lee spheres of radius 2 for all dimensions n≥ 3. This implies that the Golomb-Welch conjecture is true when the common radius of the Lee spheres equals 2 and 2n^2+2n+1 is a prime. Another consequence is that the order of any abelian Cayley graph of diameter 2 and degree larger than 5 cannot meet the abelian Cayley Moore bound.
READ FULL TEXT
