Monotonicity conjecture for the average energy of minimax spherical designs

Let $S^{p-1}$ be the unit sphere, and let $\mathcal E_{n,p}$ denote the minimum energy among designs of $n$ points on $S^{p-1}$. Define the average energy by

$$R_p(n):=\frac{\mathcal E_{n,p}}{n}.$$

Monotonicity conjecture. For each fixed positive integer $p$, the sequence $R_p(n)$ is non-increasing in $n$.

The conjecture concerns how the normalized minimax energy changes as the number of design points grows. The surrounding results establish asymptotic bounds and constructions for minimax designs, but the stated monotonicity is not resolved in the supplied text.