Currently .NET Core is only supported for Ubuntu 14.04 and when you try installing it on Ubuntu 15.10 you get the following error:
Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation: The following packages have unmet dependencies: dotnet : Depends: libicu52 (>= 52~m1-1~) but it is not installable E: Unable to correct problems, you have held broken packages.
As a workaround you can download and install libicu52 manually before installing dotnet .