There are fewer Asian airlines ordered Airbus aircarafts compared to Boeing, and there are fewer Airbuses then Boeings. Some major Asian carriers, like Japan Airlines, use only Boeing and not Airbus.
The situation is especially poor for A340. There are no more than 40 A340 in service & 60 ordered in Asia, but there are more than 100 B777 in service & 200 ordered in Asia, even Airbus A340 is much better suited for trans-Pacific routes because of ETOPS-free quad engined design, better comfort of 8-abreast Economy Class & 6-abreast Business Class, and maximum cockpit commonality with single aisles (A320).
So some questions rise: Why the sales of Airbus is so poor in Asia? Why there are so few Asian airlines ordering / operating A340 of much better design than B777? Why there are only 2 airlines ordered A380 of very large capacity even most Asian flag carriers operate B747?