Here is Barnes load data from there web site you have to go to the 140 gr bullet in their data to reach 3100fps in the 7mm rem mag. Barnes is one of the more accurate load data providers.
338 Federal ♦ Indicates most accurate load Bullet Weight: 160 gr Case Trim Length: 2.005" S.D. 0.200 Bullet Style: Tipped TSX FB Primer: Fed GM210M B.C. - COAL: 2.820" Barrel Length: 24" Case: Federal Twist Rate: 1:10" Charge Velocity Charge Velocity Load Powder (grains) (fps) (grains) (fps) Density (%) ♦ RL 7 40.0 2695 44.0 2923 99 AA 2230 48.0 2861 53.0 3089 105