I do t know if you would be gaining a whole lot with the 22 cal. I'm getting right at 3700 on my 22-243ai with fire formed brass and h4831sc and a 75g Amax and haven't found pressure yet. Have about 70 rounds down the barrel. I'm thinking the 6mm would be good. Run the stuff through a ballistic calculator and compare. My fire forming load with 75gamax is going 3550 at 3650-3700 there's not a whole lot difference in ballistics really. Like .3 moa wind at 700-800 yards in a 10pm wind. There is point of diminishing returns I believe. But I'm running a 26" barrel with a can. So I'm thinking a 6prc or saum based with a 90-105g bullet in a 20" barrel for my next build and would have roughly the same ballistics I currently get but with the shorter barrel for the can.
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