Conditions of convergence to the Poisson distribution for the number of solutions of random inclusions

Let $F$ be a random mapping of $n$-dimensional space $V^n$ over the finite field $GF(q)$ into $T$-dimensional space $V^T$ over the same field; let $D\subset V^n$, $B\subset V^T$. For the number of solutions of random inclusions $x\in D$, $F(x)\in B$ we find new sufficient conditions of weak convergence to the Poisson law as $n,T\to\infty$.