I finished the basket by adding the border. This is made from two circles of 1/2" natural cane, one on the inside top of the basket and one on the outside top. A circle of seagrass is then inserted between these two circles. Then I used 1/4" red-dyed flat cane to bind these to the top edge of the basket.
The close-up photo shows how the 1/4" cane binds the border together.