What is the largest known ordinal number $\alpha$ such that a uniform notation scheme has been developed for all ordinals up to $\alpha$ (there should be no "gaps" in what ordinals are representable), with an algorithm allowing to effectively compare any two ordinals written in that notation?
(I understand that every such scheme can in principle be extended by adding ad hoc symbol for $\alpha$ itself, but I am interested in notations that have been actually described.)