User blog comment:Deedlit11/Okay, more Turing machines/@comment-10429372-20130927154129/@comment-1605058-20131011200548

I understand what you mean. But still, I don't think anyone yet gave any proven bound for Loader's number, expect for trivial things like L<BB(L) or something.

By the way, I'm pretty sure I could make a bound using hydras for BB(<1000) if I built machine from the beginning 2-state, but building 500-or-so-state machine would be pain in the eye.