If your Q3 is 30 TDI S or 2.0 TDI edition (fitted with 16" wheels) then go for 235/60 R16. For other variants ( the ones fitted with 17" wheels ) there is no valid upsize in 17" rims and recommended upsize in 18" would be 245/50 R18.
Gautam Bakshivia Google
AUDI Q3 235/55/R17, What is the best tyre (Soft to Medium compound) offering low noise and good grip. Budget below 15k per tyre.
Considering your budgetary and other requirements,you can go for Pirelli Cinturato P7 tyre. It offers a very comfortable ride quality, superior traction and long tread life.
However, if you have an aggressive style of driving then you should go for Continental ContiSportContact 2. This is a High-Performance tyre and offers precise steering control, excellent braking and superb traction. The tread life is also quite good, but not as good as with Pirelli.