User blog comment:Ikosarakt1/Inverse busy beaver function/@comment-1605058-20140311153328/@comment-1605058-20140311180926

We can't give a lower bound which is computable and nontrivial (I believe) - every constant function, or any function which is bounded by a constant, eventually becomes a lower bound (e.g. f(n)=10 becomes a lower bound after \(\Sigma(10)\), because no larger number can be written with at most 10 states, by definition).