[tromp]

As the OEIS entry says:

> for any other busy beaver BB based on self-delimiting programs, there is a constant c such that a(c+n) >= BB(n)

This requires an information theoretic measure of program size, such as bits or bytes, whereas the TM-based BB measures in states. I don't believe there are additively tight bounds on how many states are needed to encode an arbitrary string of n bits.