UPDATED see at the end. (thanks to Prasanna)
.NET core now supports Ubuntu 14.04, 16.04, 16.10 & Linux Mint 17.
Please check the official page for all the details.
Today (May 2016) only Ubuntu 14.04 is supported.
I successfully install it on Ubuntu 15.10 by adding
deb http://security.ubuntu.com/ubuntu trusty-security main
to /etc/apt/sources-list
Once it’s done you should do:
apt-get update
apt-get upgrade
and again the command
apt-get install dotnet-dev-1.0.0-preview1-002702a
It will ask to install extra package; you reply yes and you are done!
Test by typing
dotnet --version
Enjoy!
UPDATED
Now .NET core supports ubuntu 16.04.
Please check link for more details
https://www.microsoft.com/net/core#linuxubuntu
You need to setup the apt-feed first for ubuntu 16.04.
Remove previous .net core versions from your system if any
Then install .net core sdk