Let $ϵ,\eta >0$. Does there exist a $k$ such that, given any set of $k$ primes $p_1<\cdots <p_k<n^{1-ϵ}$, each with a set $A_i$ of $\frac{p_i-1}{2}$ many congruence classes modulo $p_i$, the number of $m\le n$ such that $m\notin A_i(\mathrm{mod}{p}_i)$ for all $i$ is at most $ϵn$?