43 citations · 135 across the 14 of their papers we have counts for
6 papers · 1 filter
Optimality and uniqueness of the root system
David de Laat, Nando M. Leijenhorst, Willem H. H. de Muinck Keizer
We prove that the root system (the set of vertices of the regular -cell) is the unique optimal kissing configuration in , and is an optimal spherical code. F…
Optimality of spherical codes via exact semidefinite programming bounds
Henry Cohn, David de Laat, Nando Leijenhorst
We show that the spectral embeddings of all known triangle-free strongly regular graphs are optimal spherical codes (the new cases are points in dimensions, points i…
The Lasserre hierarchy for equiangular lines with a fixed angle
David de Laat, Fabrício Caluza Machado, Willem de Muinck Keizer
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthog…
Three-point bounds for sphere packing
Henry Cohn, David de Laat, Andrew Salmon
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a trunc…
A Breakthrough in Sphere Packing: The Search for Magic Functions
David de Laat, Frank Vallentin
This paper is an exposition, written for the Nieuw Archief voor Wiskunde, about the two recent breakthrough results in the theory of sphere packings. It includes an interview with…
Upper bounds for packings of spheres of several radii
David de Laat, Fernando Mario de Oliveira Filho, Frank Vallentin
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean…