  We study lower bounds for the Riemann zeta function $\zeta(s)$ along vertical
arithmetic progressions in the right-half of the critical strip. We show that
the lower bounds obtained in the discrete case coincide, up to the constants in
the exponential, with the ones known for the continuous case, that is when the
imaginary part of $s$ ranges on a given interval. Our methods are based on a
discretization of the resonance method for estimating extremal values of
$\zeta(s)$.
