according to this chart that's as wide as you can go on a 3" wide rim...I've heard people say that a 160 doesn't look any wider than a 150 on a 3" wide rim because it pulls the sides in an gives it a more rounded look were as a 150 looks wider an flatter.
Check with your preferred brand of tyre, as the answer to a query like that is not guaranteed. The reason is that fitment depends on the profile of the tyre. As an example the 160 I use on one of my bikes has a minimum rim width of 4.25", so is unsuitable for a 3" rim. It's better to check the brand's own website, rather than a dealer's IMHO.