User blog comment:Planterobloon/Is BAN our strongest notation right now?/@comment-30754445-20180225212126

Hyp Cos's Strong Array Notation is much stronger than BAN.

It's so strong that we can't even answer the question of how strong it is, because it surpasses all our current analysing tools. The upper parts of it are still a work in progress, but even the "lower" parts are way stronger than BAN (I think Hyp Cos' system has been analyzed to something like Psi Level 250, but it goes way beyond this. BAN, by comparision, only reaches Psi Level 180).

There's also Taranovsky's Ordinal Notation, which is rediculously strong as well. Technically it is an ordinal notation rather than a googological notation, but you can turn it into the latter simply by adding [n] after the ordinal.