Well, back in the early 90's, HP RISC was the only cache controller we found that had cache line prefetch. If you keep increasing your stride you eventually get to a big enough one that you are skipping enough cache lines that they stopped fetching.

We switched to going backwards, that fooled them for a while but now most cache controllers seem to detect forwards, backwards, and uniform strides, which is actually pretty neat.

So yeah, today it would seem that random is what you need.