I have one of these
Ruger® 10/22® Sporter Autoloading Rifle Model 31166
That comes close to matching the Tikka. Mine is slightly different than the one in the link. It is an older version without the threaded barrel, and I have it in a Hogue stock.
I found a great deal on some Burris FF-II's that I bought and have been moving some scopes around. I'm taking the 10-22 out next to dial it in at longer range with a 3-9X40 Burris.
Some things I've done that may help if anyone else is interested in shooting 22's past 50 yards. I got bored shooting at 50 yards and under. This is a new challenge for me. When I started shooting at longer ranges I had to burn a lot of ammo using the trial-and-error method to figure this out. This may save you some time and ammo.
The 36 gr CCI's work better for me past 50 yards. I can get SLIGHTLY better groups at 50 yards with match ammo. But the difference at 100 yards is not worth the more arched trajectory. I haven't tried match ammo at 200 yet. Even the 36 gr bullets are dropping an estimated 4 feet and it takes a lot of dial twisting. With the equipment I have I don't think I could get on target that far with slower match bullets.
And for unknown reasons none of my rifles shoot the 40 gr CCI ammo as accurately. It's close, and there isn't much difference in trajectory. It would only mean a few more clicks on the scope, but the accuracy just isn't as good in MY rifles. Your rifle may be different.
I do have a 15 MOA rail ordered for the 10-22. Once it comes in, and I mount a different scope on it I may give match ammo a look at longer range. But even if the ammo is more accurate, I'm not sure I can do any better than that.
100 yards is pretty easy. I zero at 50. When I go to 100 yards every scope I've used with multiple aiming points has one hash mark that gets me on target at 100. Even many plain duplex scopes are on at 100 if I use the point where the reticle changes from thick to thin as my aiming point.
I've used a CDS type scope with dials on it in the past. That system works, but I've done just as well with a traditional scope by just removing the caps and twisting the dials. Once zeroed most scopes will allow you to mark where it is zeroed so it is easy to return. With a 50 yard zero 16-18 clicks have gotten me dead on at 100 with multiple rifles and scopes with the 36 gr ammo.
When I go to 200 yards I have to twist the dial one complete revolution plus 15-30 more clicks. That does vary depending on the scope, the mounts, and rifle. But if someone wants to try 200 yards without specialized gear I'd start there and that should get you on paper. It's a good idea to use a big target at first.
One last thing. Don't try this on a windy day. I typically get to the range at sun-up when the wind is calm. By 10 AM there is often enough of a breeze to move bullets way off target.