I think covering numbers (of the unit ball) is the right way but I think about this question for a few days now.

I think covering numbers (of the unit ball) is the right way but I think about this question for a few days now and a hint would by nice….

Let $B_{1}$ be the unit ball in $\mathbb R^d$ and let $A \subset B_{1}$ be a finite set.

Denote $\ell=\lvert A\rvert^{-1}\sum_{a \in A} R(a) $ where $R:A \to (0,\infty)$ is a function such that for all $a \in A$,

$$R(a) < \inf_{a' \in A \setminus \{a\}} \lVert a-a'\rVert.$$

We need to prove that

$$\lvert A\rvert \le \left(\frac{4}{\ell}\right)^d.$$

Just a hint will be great.