An equiangular tight frame (ETF) is a sequence of vectors in Hilbert space that achieves equality the Welch bound and so has minimal coherence. More generally, an equichordal fusion (ECTFF) equi-dimensional subspaces Conway, Hardin Sloane’s simplex bound. Every ECTFF type optimal Grassmannian code, is, packing space. We construct ECTFFs by exploiting new relationships between known ETFs. Harmon...