OK. Now I think I know what we're discussing. 5" x 5" squares and maybe 8' x 8' net altogether? supported by uprights and a crossbar?
I put one of these together in Spring 2008 at my house. I have a redwood tree which drops fairly large branches during winter storms (sometimes v-e-r-y close to the house). I used three of these branches, each 1.5 to 2 inches in diameter, and lashed them together to make a frame, then used cable ties to attach the nylon netting to the branches. The trellis spans approx. 7 feet lengthwise and is approx. 6 feet high. I raised the frame/netting trellis and stabilized the two "feet" in cinder blocks packed with sand/native soil, watered the sand/soil, and packed in more sand/soil.
I was only relying on the netting for bean and pea plants to climb up, not for anything really strong and heavy, like tomatoes. Good thing, too; it sagged like crazy. The branches are still secure, although I need to pack more sand/soil into the cinder blocks, but the nylon netting is much worse for wear; I may need to roll it and use more cable ties to secure it to the branches this year.
If so, I'll be securing it not on its edges, but on what would have originally been the second square in from the edges and the top; that's how much it has stretched from light duty thus far. If you plan to ask the nylon net to support three tomato plants across 4 feet, it may not be up to the task, even when supported by 2x4s.
I also suspect that the three plants themselves will become very entangled amongst themselves. My most successful year in growing tomatoes was in Berkeley (my back yard there was significantly warmer than here in El Cerrito, mostly due to sun exposure). I had Romas that year, and each Roma plant ended up approx. 6 to 7 feet tall and an average of 2.5 to 3 feet wide. Romas are a plum-type of tomato, great for canning, not known for being exceptionally large plants.