Harold B. Burnham and Dorothy k. Burnham's Keep Me Warm One Night: Early Handweaving in Eastern Canada (Toronto: University of Toronto Press, 1972) p. 25 shows a wool basket from Ontario in the early 1800s. It is "made of willow withes in the shape of a rugby ball" which, if your school didn't have a team and you've never seen one, is like a chubby football. The basket is 50 cm (19.7 inches) long with a diameter of 32 cm (12.6 inches). There is a square hole in the top that measures perhaps as wide as a third of the total length, perhaps a little more.
I assume that compared to a typical open-topped basket, this basket has the advantage of keeping the wool inside and not snagged by branches or borne away by wind. I find the design attractive.
The authors note "this type of basket is well known in Scotland, and another smaller example has been seen in Cape Breton (Mackley Collection)....Baskets of this type were also used when teasing wool."
John Mercer's The Spinner's Workshop: A Social History and Practical Guide (Dorchester: Prism, 1978) p. 80 refers to the same type of basket but only in the context of preparing wool with hand cards: "The Highland Scots kept their rolagan [rolags] in a special container, the mudag; unaccountably oval, like a rugby ball, it had a hole in the centre of its side for the passage of the wool."
The shape makes more sense tucked under the arm out in the fields than it does resting on the floor indoors.