Maximum compatible kernel version

Solution 1:

• I would recommend going with last one prepared for same release (16.04 Xenial), current:

  http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.4.13-xenial/

• Only if you are looking to submit a bug report against kernel, then you should try the bleeding edge upload (including rc) to include results in the report, current:

  http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.7-rc2-yakkety/

We can't say compatible/or not (for example v4.4.8-wily with Xenial). You can almost run any kernel on any release when when they have same major release (4) and somehow close minor release (4/7). The only difference is that *-xenial kernel releases had passed some QA/Tests prepared for same Xenial release, no more no less.

Solution 2:

This might help: http://people.canonical.com/~kernel/info/kernel-version-map.html

Currently the lastest out of the box ubuntu 16.04 kernels are based on 4.4.8

Ex. 4.4.0-22.39 Ubuntu-4.4.0-22.39 4.4.8

You'd likely best be served by sticking with the kernel that comes with Ubuntu. If the AMD drivers are an issue I've heard others recommend sticking with 14.04