Suppose $A=\{w_1,\dots ,w_n\}\subset S^2$ maximises$$\prod _{i<j}|w_i-w_j|$$over all possible sets of size $n$. Is it true that$$\underset{C}{\max }||A\cap C|-{\alpha }_{C}n|=o(n),$$where the maximum is taken over all spherical caps $C$ and ${\alpha }_C$ is the area of $C$ (normalised so that the entire sphere has area $1$)?