For the computational model where only additions are allowed, the Ω(n^2 n) lower bound on operations count with respect to image size n× n is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proofs are based on a specific result from the boolean circuits complexity theory and are generalized for the case of boolean ∨ binary operation.