Year: 2026
Type: preprint
Abstract: This paper reports an improved numerical lower bound for packing 203 equal spheres in a unit cube. Let r denote the maximum common radius of equal non-overlapping spheres that can be packed in a unit cube. For N = 203, the configuration currently listed in Packomania has a feasible radius of approximately r = 0.088145402159. Starting from this public configuration, we perform further numerical optimization and obtain a new feasible configuration with r > 0.088145634693. The final configuration is checked by an independent verification program using 100-digit arithmetic. All 20503 sphere-pair constrains and all 1218 sphere-wall constraints are satisfied. The coordinates of the new configuration and the related programs are provided as supplementary material.
Source: arXiv (Cornell University)
Author: Lu, Peng
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221821323