In the past I've grown them in a compost bag with the sides rolled down when starting them off.
With only 4 inches of compost to start with and as the potato has grown just roll the sides up a bit and add more compost.
Have since tried planting them with next to no 'Chits and with 3" Chits and it seems to make no difference. They all grow.
One thing I can promise is the deeper the deeper the container, the more potatoes you will get. Assuming you almost cover the foliage with compost as it keeps breaking through.
Cant wait ... new potatoes with melted butter and a bit of mint !