If you are going to make your own frame make it oversize. This will allow you to use longer springs. If you go overboard on this, you can extend springs using S hooks, or loops of 3mm braided nylon cord.
A gymnastics trampoline typical has a pre-tension on the springs (no one on the mat) of about 40 lbs. Garden tramps use shorter springs and are tensioned to about 25 lbs. Because the spring is shorter, the forces increase more rapidly, so they start at a lower force.
Music wire springs are best. They can stretch 200% (10" becomes 20") But they are expensive, and being high carbon steel they rust. If your tramp is outside, see if you can get them powder coates.
In designing your frame, consider a 200 pound jumper, who depresses the mat 3 feet, and jumping 21 feet. That means he's pulling an average of 7 g's, but it will peak at up to 14 g's So 200 lbs * 14 = 2800 lbls DOWNWARD force. But the mat converts that into an INWARD force, So your frame has to be able to withstand that kind of force.
This is why the heavy tubing.
Here we can get used telephone poles for cheap. I'd give serious thought to buying 4 poles ($28 each) and setting them as the corners. Use the bottom end.
Then put a chunk of pole at ground level and at just below mat level horizontally to keep the forces from pulling the poles over.
You can put the smallest ends as side poles. They bolt to the outside of the brace poles.
The rectangular tube that holds the springs is bolted to the uprights of the poles a few inches above the horizoneal bracing poles. Trim the upright poles a frame height so they don't make puttin mats in such a pain. Bolt lighter weight tubing to the uprights. These become your net supports. 1.5" thinwall 12 ga tubing is probably enough. You want them to be a bit springy.
You can buy foam insulstion for piping. Put these on the net poles. Might be able to repurpose pool noodles.
Ideally you want the net to be supported so that it's a few inches from the poles. If the net has a stiff core (1/8" aircraft cable) you can set the net length such that when someone hits it, the force is transfered by the cable to all the adjacent posts.
One option for the net is to use plastic safety fence instead. It's strong. The holes will bite fingers, and will teach the kids to try not to actuall run into it.
