Boxes of 20 that is.
Edit 1: Petition for an extra column in the vault besides Armour, Weapons and Materials called Heavy Ammo. Exclusively for boxes of Heavy and this slot will have infinite space. (As well as more Vault space overall of course)
Edit 2: Hopefully this trending post will be stumbled upon by one who may be named the Heavy Ammo God
Edit 3: Thanks for all the replies its been fun :)
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240, so each character has 80 packs