If you are looking for a specific story associated with that number, it likely stems from one of the following:
Mr. Peterson’s house is consistently numbered 115 in concept art and the final game’s mailboxes. So what’s next door? Or under it? hello neighbor 116
No, not officially. However, there is a fan-made mod called "Alpha 116 Restoration" that attempts to recreate the lost alpha build. If you search for "Hello Neighbor 116 download" and find a file under 2GB, it is likely this fan mod, not the official game. If you are looking for a specific story