number theory - What is the effective lower bound on gaps between zeta zeros?

In this question here:
Upper bound on differences of consecutive zeta zeros
by Charles it is said that: "There are many papers giving lower bounds to:

$$\limsup_n\ \delta_n\frac{\log\gamma_n}{2\pi}$$

unconditionally or on RH or GRH." RH stands of course for the Riemann hypothesis.

Therefore I am asking: What is the best unconditional effective lower bound for gaps

$$\delta_n=|\gamma_{n+1}-\gamma_n|$$ between consecutive non-trivial Riemann zeta function zeros?