Ok... I can only remember that we had the usual oriental pattern things in the living room and under the dining table. So at grandma/grandpa’s and my parents’ place too. I already thought it was rather lame as a child because you couldn't see the beautiful parquet anymore ;) They were huge, at least your desired 3x4m, I don't even want to know what they cost.
If you sit a lot on the floor without underfloor heating then I get it :) I assume you’ve already looked in the really big furniture stores, right? They’re always different locally, for us Porta and Zurbrüggen, in Munich I would go to Segmüller. But of course call beforehand to see if they have something in that size.