Some say 223 or 556 or multi or 6.8, I think something has to be there. Doesn't really matter as long as it doesn't say pistol. As I understand, if it's a pistol, you cannot put a buttstock on it and turn it into a rifle. Once a pistol, always a pistol. If you build a SBR, you'll have to get that engraved on the lower, but once you get the tax stamp for the SBR, you can have as many short uppers as you want, at least that's my understanding of the rules. It's still just one rifle. I don't know if you can legally put a 16" or longer barrel on a SBR lower.
Anyway, back to your original question, you can build a 6.8 upper on a 223 lower.