Hans, a trub is like a #2 washtub in size, about 40cm deep and around 80cm diameter. The totes I use are 22cm wide, 38cm long and 38cm deep. Just about any size can work, depending on how many slips (plants) you want per container.
You can even use 15cm clay pots (one plant per pot in that case). Leaf nodes on the vine will turn into extra plants if you put the node down into soil, I have a friend in NZ that has grown his sweet potatoes this way for years, he usually gets a bushel per plant by burying the leaf nodes as the vine grows. He leaves the growing tip exposed so the vine will continue to extend.
Tubers of sweet potatoes are very similar in growth patterns of regular potatoes, they are swollen areas of single roots so the more roots in the soil, the potential is there for more sweets to form.
In my area our growing season starts at the middle of April and continues through November, with our harvest coming in the first week of December, we harden them for three weeks then put them in storage in a
root cellar, they last until we either run out or the new harvest is in the soil.
You could use the store bought, narrow balcony containers as long as they were deep
enough.
Redhawk