I can't speak for the .222 Remington but I have shot a lot of 52 grain bullets in a .223 and .22-250. Here are the results to date.
The Berger #22408s and Sierra # 1400 bullets are flat based.
The Sierra #1410 is HPBT.
Remington 700 .22-250 26 in barrel 1:14 twist:
Bullet------ Weight - Powder --- Avg.---# Grps --- Best Load ---Velocity
Sierra # 1410 --- 52 ---- RL-15 ---- 0.479 ----140----- 0.208 ------- 3463
Sierra # 1410 --- 52 ---- N140 ----- 0.416 ----28 ----- 0.276 ------- 3550
Berger #22408 --52 ---- RL-15 -----0.378 ----186----- 0.142 ------- 3362
Berger #22408 --52 ---- N140 ----- 0.373 ----25 ----- 0.258 ------- 3600
Sierra # 1400 ---53 ---- RL-15 ---- 0.289 ----95 ----- 0.165 -------- 3412
Sierra # 1400 ---53 ---- N140 ----- 0.346 ----109 ---- 0.184 --------3419
With a Savage 12 LPV .22-250 26 inch barrel 1:12 twist:
Bullet------ Weight - Powder --- Avg.---# Grps --- Best Load ---Velocity
Berger #22408 --52----RL-15 ---- 0.407 ------58 ------0.232 ------- 3536
Berger 322408 --52----N140 -----0.411 ------46-------0.202 -------3702
Nosler #53294 --52----N140 -----0.417 ------39 ------ 0.293 ------ 3289
Sierra @ 1400 --53 ----RL-15 ---- 0.365 -----35 -------.0201 -------3300
Results with the .223 are similar, but with different powders:
Best results are with N133 with Berger #22408 52 gr with a 0.255 average for 83 groups.
The other Berger #22408 52 gr load averages with N130, CFE223, H4895, and H335 are in the mid 0.357, 0.339, 0.484 and 0.441 respectively.
Sierra #1410 52s average 0.0377 with N133, 0.421 with H335, 0.440 with CFE223, and 0.459 with H4895.
Sierra #1400 53s average 0.357 with N133, 0.366 with H335 and 0.366 with CFE233.
I hope this helps.