Assume you have a set of unique values $V$ with a known distribution (e.g. Normal, Uniform) but unknown size $|V|$.
Assume you have function $O(t)$ that tells you the value $v \in V$ that is closest to the target value $t$
If you generate another (smallish) set values $T$ under the same distribution, I feel that you can determine an approximation of $|V|$, given $|T|$, and the RMS or something of $T-O(T)$
Is there a formula?
V = [0.090, 0.135, 0.288, 0.413, 0.434, 0.715, 0.717, 0.797, 0.841, 0.904] (actual set) T = [0.096, 0.767, 0.900] (generated values) O(T) = [0.090, 0.797, 0.904] (closest values to T in V) error = [0.006, 0.030, 0.004]
The assumption is that as $V$ grows, the error will shrink.