In the case of large sets, there is a result of Le Anh Vinh, which states that:
$$I(P,L) \leq q^{-1} |P| |L| + q^{1/2} |P|^{1/2} |L|^{1/2}. $$
Here, $q$ is the order of the finite field. Note, however, that this is worse than trivial when $|P|\times|L|$ is smaller than $q$.