The Vault-Tec terminal in the Citadel lists Vault 76 as a "control" vault, with 500 occupants. The vault was designed to open 20 years after a nuclear war, and was among the seventeen known control vaults, meaning that it was used as a baseline to compare to experimental vaults. It is also mentioned in one of the alien captive recorded logs (no.13) recorded by Giles Wolstencroft, a Vault-Tec official who was abducted while inspecting the vault's construction site. In Fallout 4, the newsreader in the prologue mentions Vault 76 debuting in 2076 in honor of America's tercentanary when discussing Vault-Tec's plans to expand.
Official Vault-Tec Info (from Computer at the Citadel)