In practice, f10 or higher will be better
I recently bought the FE 70200 G OSS. I use it on my NEX-7, and I am very impressed with it. Compared to the SEL18200 I had been using, this 70-200 G lens is quite a bit sharper at any focal length it covers. Below 70mm, theSEL18200 is still probably just about as sharp as any other zoom you can put on the APS-C camera, although primes are a different story of course.
I had done some tests to find the best aperture setting for the 70-200 G at 200mm. The test target I used at first was an antenna tower a couple hundred feet away, jam-packed with antennae and cables and all sorts of stuff. When I compared my findings with the graph seen here, there was a big discrepancy. After thinking it over, I decided that I had allowed depth-of-field to influence my findings. I dug out some old 35mm slides, and picked out one with sharp lines and corners, then taped it to the window. Different findings now, and consistent with what is shown here.
At 200mm, f4 is to be avoided, but most all of the blurriness is gone by f4.5. From f5.6 through f8 there was almost no perceptible change, and only a very slight decline in sharpness at f9, barely perceptible. Even at f11 you had to look for the loss of sharpness to see it. At f14 it was more obvious. I think that the graph here exaggerates the differences, not because of anything related to the metric that DxOMark uses, but because perceptually, one lens has to be nearly twice as sharp as another before the difference is readily apparent. This probably is true for sensor resolution as well.
For this lens, if you need any depth of field at all, f10 and f11 are best, notwithstanding what this graph suggests. f13 and f14 are still good, if you need depth of field.