OK, I thought we weren't going to go any further and the discussion would end, but I see that wasn't the case. So here goes. Please note I am going to GENERALIZE about mid-sized Standard Load passenger car tires made of polyester and steel (and nylon, of course, the subject of this discussion).
Why all the caveats? So that when people look to verify what I wrote (and I encourage people to do so), they be able to spot exceptions - and there are plenty out there.
And let me state clearly, I encourage any skeptics to call the tire manufacturers to check on what is below. I used to answer those questions for one of those manufacturers, and I will tell you that wording the responses was done very carefully - and sometimes we would not answer the question because of the way it was worded. In other words, "Your mileage may vary".
So here's a summary for mid sized (about 100 LI) Standard Load passenger car tires made of polyester and steel (and nylon):
S rated tires don't need cap plies.
Exception: Some tire manufacturers produce S rated tires with a cap ply. Why? Because tires with cap plies hardly ever fail from the dreaded belt-leaving-belt separation - aka tread separation.
T rated tires will have cap strips - nylon overlays on the belt edges - not a full cap ply. These strips will not be listed as part of the construction on the sidewall of the tire.
Exception: As with S rated tires, some tire manufacturers put on cap plies on T rated tires. Another exception is that some tire manufacturers live a little closer to the edge and don't use cap strips.
H rated tires need a full cap ply (and the exception here is those that live dangerously will only have cap strips)
V rated tires will have 2 cap plies. I don't know of any exceptions, but I assume there must be.
W and Y rated tires have have 3 layers of cap ply at the edge edges and 2 across the rest of the belt.
Note: Nowadays, cap plies are applied in a thin strip that is spiraled on. It is possible to apply as little or as much depending on the traverse speed of the applier.
You won't find 3 layers listed on the sidewall of W and Y rated tires and you probably won't have any tire manufacturer admitting to 3 layers
Second Note: What about Z rated tires? I'm not going to talk about them because Z is an odd duck. It is open ended. Technically, W and Y rated tires are Z rated tires with a restriction, but there are true Z rated tire - tires that are rated to speeds higher then 149 mph, but the exact rating speed is defined by the tire manufacturer. Each is an individual case.
Third Note: U speed rated tires. Sharp eyed readers will note that the speed rating chart includes a U speed rating between T and H. So why aren't there any U speed rated tires?
It turns out that in order to pass a U speed rating, you are almost obligated to use a cap ply - and if you do that, the tire can pass an H rating, so why not call it that?
As I pointed out earlier, some tire manufacturers use cap plies on S and T rated tires. One of the lessons from the Ford/Firestone thing some years back (has it really been 13 years?) is that tires with cap plies fail at a much lower rate (it's on the order of 10 fold or more) - and since these failures are the source of all the lawsuits (not to mention recalls), many tire manufacturers have chosen to use cap plies even when they are unnecessary to pass the speed rating test.
And another little wrinkle that I find interesting: Small tires are easier to pass the speed rating test than large tires. It is common for the larger tires to be reinforced with those cap strips and cap plies while their little brothers in a smaller size are not.
If you want to verify this (and I encourage you to do so), call the tire manufacturers. You will have to be careful about the question you ask as you might trigger their defense mechanism and get a "company proprietary" response. I suggest you ask about the construction of a specific tire (meaning make, model and size).