Intel Dual BandWireless-AC 3168 does not work on Ubuntu 16.04

This adapter is supported since kernel 4.6.

The kernel version in Ubuntu 16.04 is 4.4.

You can install kernel 4.8 to Ubuntu 16.04 this way:

sudo add-apt-repository ppa:canonical-kernel-team/ppa 
sudo apt update
sudo apt install linux-generic-lts-yakkety
sudo add-apt-repository -r ppa:canonical-kernel-team/ppa

Reboot after you do it.

After the linux-generic-lts-yakkety package appears in main Ubuntu repositories (it should happen soon) it will start getting updates.

You also need to install firmware this can be done by

wget http://mirrors.kernel.org/ubuntu/pool/main/l/linux-firmware/linux-firmware_1.161_all.deb
sudo dpkg -i linux-firmware_1.161_all.deb