sunny 16 rule for ambient sunlit scenes gives exposure ISO 100, f/16, 1/100th sec approximates to f/11, 1/180th
now we really do need to resort to using a 2 stop ND or polariser, which will give ambient exposure of f/5.6, 1/180th sec
now we need to underexpose sunlight, so need to set actual aperture to f/8-f/11 depending on desired amount of under-exposure
now to calculate flash output needed, if we set aperture to f/8, this is really f/16 taking into account the filter, and if using direct flash 2m from subject, this means flash output GN must be at least 2×16 = 32(m) at ISO100, easily within the realm of most external flash units, but in-camera flashes won't have enough power (they usually have GN 11-13 in metres).
the difficult starts to arise when using flash to bounce or through softbox or at a distance, then you really need more powerful flashes.
the other difficulty is if you really want to use a wide aperture, the solutions to this are either:
use a medium format film camera with flash sync at 1/500th sec, this will allow aperture of f/6.3, 1/500th for ambient light exposure, but with polariser, this becomes f/4.5 and thus to under-expose ambient we can set an aperture of f/6.3-f/8.
use a camera-flash system that allows use of high-speed flash sync mode (although the higher the shutter speed, the less maximum flash output is available - so move it closer or get the highest output flash).