Universal optimality of Kerdock spherical codes beyond 16 dimensions

Ascertain whether Kerdock spherical codes in dimensions greater than 16 (i.e., dimensions 2^{2k} with k ≥ 3) are universally optimal, meaning they minimize energy for every absolutely monotonic potential function on the sphere.

Background

The paper proves that the optimal 288‑point code in R16 (the Nordstrom–Robinson spherical code) is universally optimal, while noting that D4 (k = 1) is not universally optimal.

For Kerdock spherical codes in higher dimensions, the authors do not know whether universal optimality holds, though they suggest similar techniques may apply if it does.