Density of binary disc packings: lower and upper bounds
Metric Geometry
2022-06-07 v3 Computational Geometry
Abstract
We provide, for any , lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius and . The lower bounds are mostly folk, but the upper bounds improve the best previously known ones for any . For many values of , this gives a fairly good idea of the exact maximum density. In particular, we get new intervals for which does not allow any packing more dense that the hexagonal packing of equal discs.
Cite
@article{arxiv.2107.14079,
title = {Density of binary disc packings: lower and upper bounds},
author = {Thomas Fernique},
journal= {arXiv preprint arXiv:2107.14079},
year = {2022}
}
Comments
C++ code and sagemath worksheet in ancillary files. Relies on results provided in arXiv:2002.07168