Papers › Exact semidefinite programming bounds for packing problems
Exact semidefinite programming bounds for packing problems
Maria Dostert, David de Laat, Philippe Moustrou
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are unique up to rotations. In particular, we show that the configuration coming from the 𝖤₈ root lattice is the unique optimal code with minimal angular distance π/3 on the hemisphere in ℝ⁸, and we prove that the three-point bound for the (3, 8, ϑ)-spherical code, where ϑ is such that cosϑ= (2√(2)-1)/7, is sharp by rounding to ℚ[√(2)]. We also use our machinery to compute sharp upper bounds on the number of spheres that can be packed into a larger sphere.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections