In this post(Integers represented by powers of 2), I describe what I now know is similar to a covering system, where any integer can be represented by
$$\{ \frac{(-1)^k(2^{k-1}) + 1}{3} \pmod{2^k} : \forall k \in \mathbb{Z} \}$$
That is, all integers fall into the residue classes
$$ \{ 0 \pmod{2}, 1 \pmod{4}, -1 \pmod{8}, 3 \pmod{16}, -5 \pmod{32}, ... \}$$
Is there a word for a covering-system-like thing that doesn't have a finite number of residue classes, but an infinite number of residue classes that are, I don't know the word, but possibly "constructible"? The definition in Wikipedia for "Covering System" (https://en.wikipedia.org/wiki/Covering_system) specifically mentions "finitely many residue classes".
Thank you.