The wiki article about the Battle of Lake Poyang states ridiculous high numbers of troops for a medieval battle. How were they able to supply and command these large forces at that time? Or is there a catch that I can't see?
Sources from the early modern era and before are generally speaking not reliable when it comes to numbers of troops in a given battle. It is surprisingly difficult to count an army that's large enough that the troops can't be seen all at once. Here are some threads on this general subject:
and any detailed scholarly discussion (i.e. not wikipedia, bless it's heart) will have an analysis of the figures presented in sources and not just take them at face value.
An extension of OP's question, how large an army could generally be fielded by nations with that tike's technology, and which inventions increased this amount?