Consideration was given to the problem of maximum achievable precision of linear systems with discrete state and output controllers. The external perturbations affecting the system are the bounded step-type and harmonic (of unknown frequency) vector functions of time which the control theory regards as standard. The condition for asymptotic stability of the closed-loop system is the only requirement on the controllers aside from their physical realizability. Therefore, the conclusions of the present paper apply to the entire set of the discrete stabilizing controllers, no matter what method was used to design them.