As per https://github.com/travis-ci/travis-build/blob/master/lib/travis/build/script/csharp.rb#L152 and https://packages.microsoft.com/ubuntu/16.04/prod/dists/xenial/main/binary-amd64/Packages, the only available version of dotnet-sdk-3.0 is 3.0.100-1 which 3.0.0* doesn’t match.
So use a non-fully-qualified version:
dotnet: 3.0
this will cause the installation logic to request dotnet-sdk-3.0, without a specific version number.
@Joshua-Anderson, according to https://dotnet.microsoft.com/download/dotnet-core/3.0, 3.0.100 is the latest release of .NET Core 3.0.0 SDK (as of this writing). So when seeing 3.0.0, the logic should request the package in a way that matches it.