Mat Testing:
All mats will stretch over time unless they are Permatron.
The question is..... how much time!
The rebounder mats ability to resist stretch is directly related to the types of springs, the G force it puts on the mat and the type of mat.
A high end mat with cheap springs is about like putting expensive tires on a old, run down car.
Avoid nylon rebounder mats....they are gonna stretch more than any other mat besides canvas mats.
Canvas mats tend to start rotting and rip the most.

If you have bad knees, back, or hip problems AVOID canvas mats.

If you are going to rebound outside in the direct sun, avoid blue Permatron mats.
These are not UV resistant and don't have the UV ratings as the black mats.
Blue mats can wear out faster and stretch out quicker.

Always make sure the stitching is seared together to avoid the common "running" of the threads
Cheaper rebounder mats do not have seared stitching.
Some rebounder companies sear their threads because they have what's known as the "running" problem.
Permatrons mats are the best. Seared Permatron stitched mats are the best.
The best threading for rebounder is 4 Ply polyeaster thread.
I recommend get the highest grade Permatron for a rebounder if you want it to last many years longer than the canvas or nylon mats.
Fuzzy Prevention:
Wanna stop getting those fuzzies on your rebounder mat and stop the mat from "fraying"?
Better stitching that is the seared type will stop the mat from breaking down prematurely.
Mats can stretch because there is not enough "tensile resistance".
Permatron mats have the most resistance.
Since Permatron mats don'tt stretch, they won't throw you off balance and will give you an "upward" lift since it does not cone in like other mat materials.
Always go for the 4 Ply polyester thread instead of nylon or vinyl stitched rebounder mats. (Note: High quality mats do not create a lot of the static like other mats. On some rebounders, when my dog jumps on it, I can't even touch him without shocking myself and shocking the dog, especially when used on the carpet. I've noticed that leaving rebounders outside in the rain helps get rid of this static but if the stitching and mat is not protected the mat might dry out and doesn't feel good to the feet like a fresh mat.

Mat Tip 
A good mat has double or triple stitched outside edges so the springs hooks never rip through the mat or stretch out giving it uneven mat tension. A good rebounder mat lets me land on the mat where the majority of my weight deforms the surface of the mat as my body never stops in a sudden force at the bottom of the bounce. The milli seconds that each type of rebounder spring lets my body go down to deform the complete surface of the mat makes the difference in the feel of one rebounder to another. All the springs working synergistically should cause this feel.
A final word on rebounder mats:
To avoid fraying or premature stretching of the mat, avoid Vinyl and nylon mat threading. My best advice is to look for a mat that has Polyeaster and is at least 2 or 3 ply threaded. 
If you are have any balance problems, you don't want a mat that is very firm suddenly around the edges and really soft in the middle of the mat. If I don't space my feet equal distance apart on some brands, such as having one foot near the edge and one foot in the middle, it can throw me off balance.

The bigger the rebounders "sweet spot" the more stable the rebounder feels. Some rebounders invert my ankles so bad from the "cone" shape it makes when I jump on it. If someone doesn't mind wearing special running shoes for pronation problems they can get away with it or, buy a rebounder that doesn't do this. I prefer rebounders that do not have On our bowling balls test we showed how dropping the ball in different spots of the rebounder gave higher or lower bounces.  So, having one foot on a firm spot near the edge and one on a significantly softer spot near the center of the mat is what I try to avoid. The Cellerciser has the least of this and teh single tiered rebounders that have the short coils like the Lymphaciser also have this.
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