Zero-sets for $H^\infty$-functions on hyperplanes in $\mathbb B^n$

Let $\mathbb B^n$ be the unit ball in $\mathbb C^n$, $n\ge2$. We put $T_a=\{z\in\mathbb B^n:(z,a)=|a|^2\}$ for $a\in\mathbb B^n$ and $T_A=\bigcup\limits_{a\in A}T_a$ for a discrete in $\mathbb B^n$ set $A$. We find a sharp necessary condition for a set $A$ to be a part of the zero-set for a function in $H^\infty(\mathbb B^n)$.