The most precise woodworking tradition in the world is in
On a smaller scale - the Shoji style of making partitions, cabinets and boxes also involves amazing precision and ingenuity.
The same kinds of traditions are found in
It is not very clear which is older.
On another continent, the traditional Swiss cabinetmakers and clock makers had a very fine woodworking tradition - they built cuckoo clocks and complicated wooden mechanisms with great precision.
The clear winner is Japan (lumped together with China)