You can't usually download this. I haven't been able to find it. However, the SDK (all of them, .NET, Java, etc.) are all on the ArcGIS Install CD.
"Installation ended prematurely because of an error.."
General availability for the "ArcObjects 10.4 SDK for .NET" is not until the week of February 15, 2016. Once the SDK is available you would download it from MyEsri (same as 10.3.1).
So for example for 10.3.1 the download would be here (however, you need to log in first):
What flavor of Visual Studio will allow the "ArcObjects SDK for the Microsoft .NET Framework" to be installed? Visual Studio Community 2015 is not supported. The posted requirements for VS software products that are, at the time of this posting, 3-4 years old seems like a real issue because they are no longer available.
Which version of the "ArcObjects SDK for the Microsoft .NET Framework" are you trying to install? The requirements for the latest release (10.4.0) can be found here (scroll to the bottom of the section):