Addendum to Exercise 1.21 from the lecture notes

Recall the definition of a hyper-assignment from Exercise 1.21: A function A: V --> {0,1,*}. Suppose you want to succinctly represent the set of non-satisfying assignments of a CNF formula F as the union of "few" hyper-assignments. Can you give a good bound on how many such hyper-assignments you need?