I installed ubuntu 15.10 2 days ago without problems, I used uefi boot from rufus USB sttick.
In your case it looks like the drive isn't recognized at some point.
What kind of harddrive is in your NUC and does the BIOS recognize your disk correctly?
I have a Samsung 950 pro ssd. The ssd is recognized by the legacy bios, but not by uefi.
My usb is recognized by both the legacy and uefi.
I made the live usb on OS X with the dd command
may hold a solution to your issue, at the bottom of the page, by Darckhart
I recreated the live usb with rufus (GPT partition scheme) and disabled legacy boot in bios.
Next I reinstalled Ubuntu, after which I still couldn't boot to the ssd. I went back to the live usb and installed the boot repair tool, I chose all the standard settings, except disabling secure boot.
Now it works :-)