Enumeration yields 1579 non-isomorphic maximum independent sets in J±(12,4) giving non-isometric kissing arrangements of size 840, with a proof that for n≡2 or 4 mod 6 all such sets arise from Steiner quadruple systems.
What are all the best sphere packings in low dimensions?
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
cs.IT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Kissing arrangements of 840 spheres in R^12 admit positive-dimensional families of non-isometric realizations via flexible 48-systems in each 60-point block with fixed bridges, enabling a numerical 841-sphere configuration via Riesz energy optimization.
citing papers explorer
-
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Enumeration yields 1579 non-isomorphic maximum independent sets in J±(12,4) giving non-isometric kissing arrangements of size 840, with a proof that for n≡2 or 4 mod 6 all such sets arise from Steiner quadruple systems.
-
Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere
Kissing arrangements of 840 spheres in R^12 admit positive-dimensional families of non-isometric realizations via flexible 48-systems in each 60-point block with fixed bridges, enabling a numerical 841-sphere configuration via Riesz energy optimization.