A NOTE ON TOTALLY SYMMETRIC EQUI-ISOCLINIC TIGHT FUSION FRAMES

Consider the fundamental problem of arranging $r$-dimensional subspaces of $\mathbb{R}^d$ in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are \textit{totally symmetric}: any permutation of the subspaces can be realized by an orthogonal transformation of $\mathbb{R}^d$.