Optimal line packings from association schemes

We provide a general recipe that leverages association schemes to construct optimal packings of lines through the origin. We apply this recipe to association schemes corresponding to general Gelfand pairs before focusing on the special case of group schemes. In this setting, optimal line packings are naturally characterized using representation theory, which in turn leads to necessary integrality conditions for the existence of equiangular central group frames. We conclude with an infinite family of optimal line packings using the group schemes associated with certain Suzuki 2-groups. Notably, this is the first known infinite family of equiangular lines arising from nonabelian groups.

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