To start with, read the info in this site:
223 Rem + 223 AI Cartridge Guide
There's one error in that site:
The 5.56x45 is built to NATO specs, rated to 60,000 CUP max pressure
That should be 62,366 psi; EPVAT piezo transducer pressure gauge not the SAAMI 52,000 copper crusher "cup" one. This has oft times been a confusing issue for decades. Note also that the NATO pressure system is different than the SAAMI one that specs the .223 at 55,000 psi.
Here's what I've gleaned from people getting best accuracy with the .223 Rem (5.56 NATO) at long range 600 to 1000 yards) since I was one of the first few to shoot them in competition back in 1971:
* Use new cases. As bolt faces on the semiautos are oft times not squared up with the chamber axis, fired cases from them will have out of square case heads. They don't shoot bullets as accurate as new cases whose heads are typically quite square. If you choose to use fired cases, full length size them in a standard die whose neck is honed out to 1 to 2 thousandths smaller than a loaded round's neck diameter. The link above suggests one from Forster. Use a gauge to measure how much the fired case shoulder's set back and adjust the die so it's no more than .003" back from its fired position.
* Powder should be a short length stick/extruded type. Nobody gets best accuracy with any ball powder. While slower ones will shoot a given bullet out faster, they won't leave with the most consistent muzzle velocity. Match winners and record setters prefer accuracy over wind bucking; you can correct for wind but not for poor accuracy. Weigh charges to a 1/10th grain spread in charge weight; they don't have to be exact.
* Seat bullets to a depth that gives best accuracy. They may not fit in the magazine so you'll have to single load them. If they must be seated to fit the magazine, so be it.
* Do not crimp the case mouth onto or into the bullet.
* Shoot at least 15 shots per test load to get a statistically significant measure of the load's accuracy. There can be a 300% to 400% spread in group size from smallest to largest shooting only 3 shots per load. A 200% to 300% spread with 5 shot groups. 15 shot groups have about a 15% spread across several of them. Shoot twenty groups of each shot count per group and you'll understand. The first group shot is not always the smallest; nor the largest, for that matter.
* If you choose to shoot a few 3- or 5-shot groups with each load to asses its accuracy, pick the largest group's size for each load to represent its accuracy you can count on most of the time.
* Most important; you're the biggest variable in group shooting if you're holding onto the rifle as it rests atop something on a bench top.
Sierra Bullets' accuracy load that did well in several 20" AR type barrels:
23.5 grains of Viht N140 with their 80 grain bullet.
24.0 grains of Viht N140 with their 77 grain bullet.