Just to be clear, the note 3 is not a galaxy nexus, even if it is by the same manufacturer. It would not be a full installation unless you have a way to dock it, in which case you would just use "ubuntu for android" which does not depend on model or manufacturer. If you are talking about ubuntu touch, you have to check for support, which is something that I do not see. A better place to check for a custom support version would be xda-developers.com
Just to be clear, the note 3 is not a galaxy nexus, even if it is by the same manufacturer. It would not be a full installation unless you have a way to dock it, in which case you would just use "ubuntu for android" which does not depend on model or manufacturer. If you are talking about ubuntu touch, you have to check for support, which is something that I do not see. A better place to check for a custom support version would be xda-developers.com