  We obtain a new lower bound on the size of value set f(F_p) of a sparse
polynomial f in F_p[X] over a finite field of p elements when p is prime. This
bound is uniform with respect of the degree and depends on some natural
arithmetic properties of the degrees of the monomial terms of f and the number
of these terms. Our result is stronger than those which canted be extracted
from the bounds on multiplicities of individual values in f(F_p).
