A remarkable coincidence has led to the discovery of a family of packings of (m^2+m-2) m/2-dimensional subspaces of m-dimensional space, whenever m is a power of 2. These packings meet the ``orthoplex bound'' and are therefore optimal.
@article{arxiv.math/0208003,
title = {A Family of Optimal Packings in Grassmannian Manifolds},
author = {P. W. Shor and N. J. A. Sloane},
journal= {arXiv preprint arXiv:math/0208003},
year = {2007}
}