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PreprintarXiv licencearXiv

An Improved Lower Bound for Packing 203 Equal Spheres in a Unit Cube

  • Peng Lu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026improved,
  title = {{An Improved Lower Bound for Packing 203 Equal Spheres in a Unit Cube}},
  author = {Peng Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13978},
  eprint = {2610.13978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13978},
}
RIS
TY  - UNPB
TI  - An Improved Lower Bound for Packing 203 Equal Spheres in a Unit Cube
AU  - Peng Lu
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.13978
UR  - https://arxiv.org/abs/2610.13978
AB  - 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.
ER  -