Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to $${SL_2(\mathbb {R})}$$ , there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolume