A Family of Optimal Packings in Grassmannian Manifolds
P.W. Shor, N.J.A. Sloane
TL;DR
This paper introduces a family of optimal packings of subspaces in Grassmannian manifolds, achieving the orthoplex bound for dimensions where m is a power of 2, thus providing new optimal configurations.
Contribution
The paper discovers a new family of optimal subspace packings in Grassmannian manifolds for dimensions that are powers of 2, meeting the orthoplex bound.
Findings
Packings meet the orthoplex bound
Optimal configurations for m being a power of 2
Family of packings in Grassmannian manifolds
Abstract
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Computational Geometry and Mesh Generation · Advanced Graph Theory Research