Designs in Grassmannian spaces and lattices

DOI10.1023/A:1020826329555zbMath1035.05027MaRDI QIDQ1862267

Christine Bachoc, Renaud Coulangeon, Gabriele Nebe

Publication date: 11 March 2003

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

spherical designorthogonal group\(t\)-designGrassmann manifoldLatticeRankin functions

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other designs, configurations (05B30)

Related Items (22)

Extreme lattices and vexillar designs ⋮ Asymptotically optimal designs on compact algebraic manifolds ⋮ Finite groups admitting Grassmannian 4-designs ⋮ Designs, groups and lattices ⋮ Explicit construction of exact unitary designs ⋮ Great antipodal sets on complex Grassmannian manifolds as designs with the smallest cardinalities ⋮ Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold ⋮ Low-energy points on the sphere and the real projective plane ⋮ Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians ⋮ Codes and designs in Grassmannian spaces. ⋮ Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians ⋮ Tight \(p\)-fusion frames ⋮ Bounds for codes and designs in complex subspaces ⋮ Points on manifolds with asymptotically optimal covering radius ⋮ From low- to high-dimensional moments without magic ⋮ Antipodal sets and designs on unitary groups ⋮ Rational designs ⋮ Curve based approximation of measures on manifolds by discrepancy minimization ⋮ Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms ⋮ Unitary designs and codes ⋮ A survey on spherical designs and algebraic combinatorics on spheres ⋮ Small designs for path-connected spaces and path-connected homogeneous spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On even unimodular extremal lattices
• Spherical codes and designs
• Réseaux k -Extrêmes
• Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
• Generalized Jacobi Polynomials as Spherical Functions of the Grassmann Manifold
• On Positive Definite Quadratic Forms
• Symmetric squares, spherical designs, and lattice minima. Appendix: Two-designs and code minima by Christine Bachoc and Pham Huu Tiep

This page was built for publication: Designs in Grassmannian spaces and lattices