In the case of large sets, there is a [result of Le Anh Vinh][1], 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 $q$.


  [1]: http://arxiv.org/pdf/0711.4427v1.pdf