Just a thought, but if you want to shoot for the best possible group, you've got to go at it the right way. With iron sights, you need to use soot off a candle, etc. to blacken the sights as that will help get a better sight picture. Use the smaller aperture of the rear sight. Place your eye relative to the rear sight the same way for each shot. At least in my experience, a 6'O'Clock hold (pumpkin on the fence post) allows me a much greater degree of precision than does a center hold of a black front sight against a black bullseye.
Using a good scope greatly simplifies getting good results at relatively long range using any .22 LR rifle. As Jim Carmichael once opined, "You can't hit it if you can't see it." A scope w/ sufficient horsepower helps. As an example, I once took a Leupold 6.5x20 off a varmint rifle and put it on a Ruger 77/22. With the 4x scope that it commonly wore, I could get 10 shot groups at 100 yds. of 2.0 inches or maybe a little less. With the higher powered scope groups ran down to 1.5 inches and were much more consistent. When I blundered on some really nice Winchester T-22's, I even got a few groups that went into slightly less than an inch. It was a real shock to me as I'd not expected that rifle to do so well. When I took the Leupold off that rifle, the scope that replaced it was a nice little Weaver 2x7 Wideview. That combination was much better suited to use in the woods and fields. And, on the range, it would still produce very nice 10 shot groups at 50/100 yds. Cool.
Regardless of whether one uses iron sights or a scope, using good marksmanship techniques common to shooting any rifle for group/score are requisite to getting good groups. Unless one is really really an excellent marksman, shooting long strings of fire, i.e., 10, 15, 20, 30 rounds is really taxing. Shoot groups of 5 to 10 rounds. Look at the average of those groups as indication of what that particular rifle/ammo combination will produce on target. And obviously, use a broad variety of .22 LR ammunition in searching for the best possible on target results. There really is a difference in how different rifles shoot different brands of ammunition. And while the high grade target type ammunition typically produces good results, it is not uncommon to find garden grade and even bulk packed ammo that will produce excellent on target results with particular rifles. The above 77-22 produced some of it's best groups w/ Winchester T-22's. However often very similar results were obtained using Remington Thunderbolt .22's. Odd I know, but that's what happened.
From what I've read at this and other sites, the 15-22 does not produce the level of accuracy as might be expected from a tricked out 10-22. From my perspective, that's O.K. I bought the 15-22 because I wanted a AR-15 styled rifle in .22 LR caliber that I could afford to shoot. I had confidence in it because of it being a S&W product. So far, I have been very pleased with it. If I develop strong interest in shooting it at long range, I'll go about a development plan similar to what I'd do with any other rifle that I wanted to optimize for a particular use.
The above rambling is brought to you courtesy of a honking big 20 oz. cup of hot homemade coffee, a full night of sleep, my taxes being finished w/ nothing owed (!!!) and this being my (drum roll) off day! I take full responsibility for the opinion expressed. :-;