On sheets of conjugacy classes in algebraic groups

Let G be a simple algebraic group of adjoint type over an algebraically closed field k of characteristic p. We aim to count the number of sheets of conjugacy classes in G, as p varies. It was noted that for G_2 the sheets are the same for p=3 and for good characteristic. This leads to the conjecture of there always being a bad characteristic for which the numbers of sheets is the same as in good characteristic. Another motivation for this investigation is the fact that Lusztig strata are unions of sheets and their number doesn't depend on the characteristic. We prove the conjecture to be false.