If $P\subseteq S^2$ is a subset of the unit sphere then define the discrepancy$$D(P)=\underset{C}{\max }||C\cap P|-{\alpha }_C|P||,$$where the maximum is taken over all spherical caps $C$, and ${\alpha }_C$ is the appropriately normalised measure of $C$.Is it true that$$\underset{|P|=n}{\min }D(P)\to \infty$$as $n\to \infty$?