Grassmannian
Subspace Packing
The complex (or real) Grassmann manifold G(m,k) is the set of k-dimensional
subspaces in Cm
(or Rm).
Grassmannian subspace packing is the problem of
finding a set of N k-dimensional subspaces in G(m,k) that maximize the minimum distance
between any pair of subspaces in the set. Numerous distance functions can
be defined on the Grassmann manifold (see Barg
and Nogin, Bounds
on Packings of Spheres in the Grassmann Manifold).
This page provides the best known packings (at least to me) for various values
of k and N for the complex Grassmann manifold. For real
packings please see the excellent
tables provided by Neil Sloane. The packings are all given in .mat
format.
If you have found a better packing then send me an email to djlove
@ ecn.purdue.edu
k=1
packings The packings are stored in matrix
format where the columns represent each of the N lines. The files
are labeled codebook_m_Nvec.mat.
k=2 packings
k=3 packings
k=4 packings
k=5 packings