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

$(p,q,n,s)\in {\text R}$ 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 ${\text R}\subseteq \mathbb{N}^4$ computable?