Multiplayer game state sync

Design the real-time state-synchronization layer for a 60-player battle-royale game. Each match runs ~25 minutes; players send inputs at 60 Hz and need to see other players' positions, projectiles, and hit events with <100 ms perceived lag despite 30–150 ms RTT. The server must be authoritative (anti-cheat), and clients on flaky mobile connections must degrade gracefully. How do you keep all 60 clients consistent at scale across thousands of concurrent matches?