Joey Iverson recently posted our paper with John Jasper on the arXiv. As the title suggests, this paper explains how to construct optimal line packings (specifically, equiangular tight frames) using association schemes. In particular, we identify many schemes whose adjacency algebra contains the Gram matrix of an ETF. This unifies several existing constructions, and also enabled us to construct the first known infinite family of ETFs that arise from nonabelian groups.

John is on the job market this year, and when reading his research statement, I was struck by his discussion of our paper, so I asked him to expand his treatment to a full blown blog entry. Without further ado, here is John’s guest blog post (which I’ve lightly edited for hyperlinks and formatting):

Continue reading Optimal line packings from association schemes