Uniqueness sets with angular density for spaces of entire functions, III: how to minimize the type

This note is the third part of our work devoted to uniqueness sets for spaces of entire functions. Given a discrete set $\mathrm{\Lambda }$ with angular density $\mathrm{\Delta }$ with respect to the order $\rho$, satisfying some regularity condition, we show that there exists a type-minimizing measure ${\mathrm{\Delta }}_0$ with less than $2\rho$ discrete masses. For the case $\rho =2$, the value of the critical uniqueness type is found in geometric terms.