  In this article we prove a conjecture of A. Lubotzky: let G = G_0(K), where K
is a local field of characteristic p>5, G_0 is a simply connected, absolutely
almost simple K-group of K-rank at least 2. We give the rate of growth of
r_x(G) :={H< G| H a lattice in G; vol(G/H)<x}/~, where H_1\simH_2 if and only
if there is an abstract automorphism t of G such that H_2 =t(H_1). We also
study the rate of subgroup growth s_x(H) of any lattice H in G. As a result we
show that these two functions have the same rate of growth which proves
Lubotzky's conjecture. Along the way, we also study the rate of growth of the
number of equivalence classes of maximal lattices in G with covolume at most x.
