if i remember correctly, there is a quite large chinese/thai shop near basel station which is also open on sundays (i don't know if it is accurate) and they also have korean & japanese groceries, too.
if you have a chance to come to zurich
YumiHana
Schützengasse 7, 8001 Zurich (near main station)
and
Nishi's Japan Shop
Schaffhauserstrasse 120, 8057 Zurich
both have large selection of korean/japanese food.
here, you can order japanese groceries online:
http://www.jafoo.ch/