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Small apertures (physical size) and small f/stops (f/number) are opposites. f/stop being the ratio of the physical diameter of the aperture and the focal length. An f/1.0 50mm lens has aperture that is 50mm in diameter. An f/2 lens has an aperture wide open of 25mm, at least in theory. Modern lens designs may deviate with smaller physical apertures (e.g.. a 50mm f/2 with an aperture of 30mm) but the lens is marked as f/2 by comparison with a reference standard.
If you compare resolution for any lens over its aperture range you seen that from wide open the resolving power increases for about 2-1/2 to 3 stops, the starts decreasing again due to diffraction as the physical size gets smaller. So an f/1.4 lens is sharpest at f/2.8 to f/4 and a f/2.8 lens around f5.6 to f/8.
As the aperture gets smaller it also changes the X optical path. That doesn't affect film, but digital sensors sites are U shaped wells and the way the light rays at the edges of the frame hit them at a more acute angle affects IQ.
So there is actually sound measurebational basis for the rule of thumb with digital to not increase f/stop (reduce aperture) above f/11 but in practice in most photos the difference in IQ between the resolution sweet spot and f/22 might not be noticed or attributed to other variables such as DOF, focus etc. It's difficult to see perceptually on other than flat 2D targets because of the fact the DOF changes: perceptually a shot at f/22 seems sharper than one at f/5.6 on the 3D subject because more of it is seen in sharp focus.
Optimal results would be obtained by shooting at the f/stop with best resolution, shifting focus in multiple shots and then blending them in PP.