T1 or XPS style dots would look great on a 416.
With that budget I'm afraid you'll only be able to buy an Element/Aim-O replica which, imo, is currently the best repro brand available. Don't bother with other repros, most of them are crap.
If you can stretch your budget to, let's say, £150 you could take a look at Holosun's range of T1 style dots. They are solar powered too, so no need to worry about leaving them on or replacing batteries
Vortex is also a great and affordable RS optic manufacturer with similar prices.
They offer good lifetime warranties too!
If you're on a tight budget then Element/Aim-O as I said, I have a T1 replica that has been abused a lot and it's still working great, apart from some missing paint chips (which I do not particularly give a fuck about), dot is crystal clear. Retail price here is €70 but I got it for free from a friend