  We extend Bravyi and Smolin's construction for obtaining unextendible
maximally entangled bases (UMEBs) from equiangular lines. We show that
equiangular real projections of rank more than 1 also exhibit examples of
UMEBs. These projections arise in the context of optimal subspace packing in
Grassmannian spaces. This generalization yields new examples of UMEBs in
infinitely many dimensions of the underlying system. Consequently, we find a
set of orthogonal unitary bases for symmetric subspaces of matrices in odd
dimensions. This finding validates a recent conjecture about the mixed unitary
rank of the symmetric Werner-Holevo channel in infinitely many dimensions.
