On Tuesday, Google surprised most everyone by releasing an updated Android 5.1.1 factory image for the Nexus 7 (2013) Wi-Fi. The update was seemingly a maintenance revision (Android 5.1.1_r6) with no feature updates.
The update was available as a factory image only, but it now seems that the Over-The-Air (OTA) file has begun to roll out to units and an enterprising couple of people have captured the OTA URL so you can download and flash the update without having to wait.
The update link is from LMY47V to LMY48G, so ensure you’re grabbing the right OTA, if you’re on an earlier version update to LMY47V and you should be right to continue. You can find instructions on how to sideload an OTA here, and the link to the update is here:
Android 5.1.1_r6 for Nexus 7 (2013) Wi-Fi) – LMY47V to LMY48G