Let $\mathbb{N}$ denote the set of positive integers. We define a relation $R \subseteq \mathbb{N}^4$ in the following way:

$(p,q,n,s)\in R$ if and only if there is $S\subseteq [0,1]^n$ with $|S| = s$ such that for all $x\in [0,1]^n$ there is $y\in S$ such that $\| x-y \|< \frac{p}{q}$.

Question. Is $R\subseteq \mathbb{N}^4$ computable?