Not more than an hour ago it was reported that some users had started to receive the over-the-air update to the Google Nexus 10 tablet for Android 5.1.1. While the update is small and is likely only about bug fixes, an update that squashes bugs is just as important as that which brings in new features and functionality to devices. While waiting for the OTA to show up on a device is the safest way to ensure the update process goes smoothly and software is installed correctly, there are other options for people who would prefer to have the update sooner than later.
Flashing the over-the-air software package from the OTA download link is one way, however at this point in time it doesn't appear that the OTA download link is available for the Nexus 10 just yet. The good news is that it shouldn't be long before it pops up. Users can also flash the factory image files that Google posts to the Nexus factory image website, and as one would have it Google has done just that with Android 5.1.1 for a few other devices, which includes the Nexus 7 WiFi only model from 2012, the Nexus 7 WiFi only model from 2013, and the Nexus 10 tablet which started getting the OTA just earlier this afternoon.
All three of these devices have the factory images available as of now, which brings each device up to Android 5.1.1 build version LMY47V. As stated above the update is more than likely just about some minor bug fixes and improvements given the size of the actual OTA update package which comes in at just under 14MB in file size. Flashing the factory images is not something you should attempt to do if you're not familiar with the process, however, it isn't too difficult so long as you follow the correct set of steps, which you can find here in this handy little guide. If you've been experiencing any issues with either of these three devices after updates to Android 5.0 or 5.1, then this latest software should and hopefully will help out in this regard.