Lufthansa/Swiss/Austrian would be a good bet in F class as you get 300% M&M miles plus bonus. The problem would be round the world- does this have to be? If so not possible. However as these three airlines are "integrated partners" you would be earning the HON circle miles. So- taking this into consideration, and given the elite bonus of 25%, if you did ultra longhaul (like FRA-EZE and SIN-FRA) you would need-
FRA/EZE Apox 23K per leg- so "only" 50 legs- easy in 100 day- but the cost would be more likely closer to 250K. Surely someone will figure out a better option. The problem with RTW is how to do it with one carrier- perhaps through SQ- as you could fly SIN-FRA-JFK-EWR-SIN? The cost might be a bit much however....