We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.

翻译：我们从一个球形尺寸的球形码的距离总和中得出上下限值,当值N\sim n ⁇ alpha,0 ⁇ alpha\le 2.$时,以美元为单位计算,以美元计,以美元为单位计算。 界限来自最近专门对球形能量的通用总限制。 我们讨论了我们界限的无药可治行为,并列举了几个代码的例子,这些代码的距离总和与上界十分接近。