Probably the best bet is the DA 16-45/f4 They go for around $200 used since they have been discontinued a couple of years ago.
Something wider than 16 with equal or better image quality, at the same price is going to be a challenge. Going up $100+ you get into the wider Samyang prime lenses at 16, 14 and 10mm. There is also the Pentax DA 14/f2.8, but that is also more expensive.
There is also the Zenitar 16mm f2.8 Fisheye in a K mount. The lens is a FF fisheye, but on a cropped frame it looses a lot of the FE effect but is not totally rectilinear, but its at the $200 price point.
The older M42 lenses and original K lenses, 15mm is really the widest, and they are difficult to find and very expensive.