Any higher dimensional shift space (X, ℤᵈ) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of ℤᵈ where r \u3c d. We show here that any projectional entropy is bounded below by the ℤᵈ entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite product of a lower dimensional projection
