"Fallout 76, a new Fallout game that got an unexpected teaser trailer today, references one of the many fictitious vaults of the post-apocalyptic series’ canon. This one is Vault 76, which meticulous Fallout fans may remember being mentioned in passing in 2008’s Fallout 3.
In that game, inside the Citadel (the headquarters of the Brotherhood of Steel and staging area for the final missions of the main story) is a Vault-Tec terminal. Vault 76 is located in Virginia (or perhaps now West Virginia, given that the teaser trailer is set to “Take Me Home, Country Roads”).
As noted by Fallout wiki Nukapedia, Vault 76 is one of 17 “control vaults,” as opposed to the experimental vaults, where Vault-Tec was observing human behavior under other introduced conditions. In the teaser trailer, Vault 76 appears to be tasked with rebuilding the Wasteland and restoring civil order to it."
and EDIT: "Vault 76 is the "Missing vault" mentioned in Mothership Zeta"