As you may know, the guys from the Black Lab Software has created an Linux kernel enablement kit that permits everybody that has an Ubuntu-based system to install Kernel 4.1.6 on their system.
The development kit has official support for Black Lab Linux 4.x, 5.x, 6.x, 2015.x series, Ubuntu 12.x, 14.x, and 15.x series, as well as all of the Linux Mint 17.x series and the installation instructions are simple.
To install Kernel 4.1.6 on your Ubuntu based systems, you have to download the kit, extract the archive, set execution permissions and run the software:
$ cd ~/
$ wget "sourceforge.net/projects/os4online/files/Kernel%20Updater/kernel-416.tar.gz"
$ tar -xzvf kernel-416.tar.gz
$ chmod +x kernel-enablement-kit-4.1.6
$ sudo ./kernel-enablement-kit-4.1.6