Achievability of equality in non-Rankin bounds for Stiefel codes

Ascertain whether equality can be achieved in bounds on Stiefel codes beyond Rankin's simplex and orthoplex bounds—specifically, in the sphere-packing bounds for Grassmann and Stiefel manifolds and related unitary constellation bounds such as those derived by Henkel and by Han and Rosenthal—and, if so, construct codes that attain these bounds.

Background

The paper focuses on achieving equality in Rankin-inspired simplex and orthoplex bounds for Stiefel codes and gives constructions that meet these bounds in many cases. However, the literature contains other upper bounds relevant to Grassmannian and Stiefel coding problems, including sphere-packing bounds and diversity bounds.

The authors point out the open direction of determining whether these other bounds are tight by exhibiting Stiefel codes that meet them, which would extend the catalog of known optimal configurations beyond the Rankin-equality regimes.