9 citations · 16 across the 4 of their papers we have counts for
4 papers
On tight spherical designs
Gabriele Nebe, Boris Venkov
Let X be a tight t-design of dimension n for one of the open cases t=5 or t=7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to e…
Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14
Gabriele Nebe, Boris Venkov
The extremal 3-modular lattice with automorphism group $C_2 \times G_2(\F_3) $ is the unique dual strongly perfect lattice of dimension 14.
Construction of spherical cubature formulas using lattices
Pierre De La Harpe, Claude Pache, Boris B. Venkov
We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory…
Low dimensional strongly perfect lattices. I: The 12-dimensional case
Gabriele Nebe, Boris Venkov
It is shown that the Coxeter-Todd lattice is the unique strongly perfect lattice in dimension 12.