{"id":"hexagon/2610.00317","pdf":"https://hexagonmath.org/pdf/2610.00317v1","url":"https://hexagonmath.org/abs/2610.00317v1","tags":["math.MG","math.NT","cs.IT","msc:52C22","msc:05B45","msc:94B25","msc:05C25","Golomb-Welch conjecture","Lee metric","group ring"],"score":0,"title":"No lattice tiling of $\\mathbb{Z}^{35}$ or $\\mathbb{Z}^{805}$ by Lee balls of radius three","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.CO","summary":"We prove that there is no lattice tiling of $\\mathbb{Z}^{35}$ or of $\\mathbb{Z}^{805}$ by Lee balls of radius three. These were the only cases left open by Xiao and Zhou among the Lee balls of dimension at least three and radius at least two with fewer than $2^{30}$ points, so the lattice Golomb--Welch conjecture holds for all of them.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}