Many one design cats have a rule that precludes you from using any non-woven material for the tramp. For example, the story I heard was, it's banned on the Tornado because no one wanted to use it but it it can be an advantage under some conditions.

If you want a sort of net, there is a knitted dacron fabric (http://www.sailrite.com/Categories/Trampoline-Mesh_2).It's soft, net like and works well. HOWEVER, it's very UV sensitive. Even protected from the sun it may only last 2 years. There is also a perforated vinyl (like a solid Hobie tramp with lots and lots of holes in it) but I have not seen that material in years

Everytime I buy or build a trampoline, I look around, think about it, and decide to use some form of polypro mesh. It's light, durable, and strong. Now if someone makes that knitted fabric out of polypro, I might, reconsider