The Gigaton Ball can be used to catch Pokémon. It cannot be thrown very far, but is more effective if the Pokémon it's used on hasn't noticed the player. If so, it attempts to catch the Pokémon with a catch rate modifier of 2.75×. Otherwise, it has a 2.5× modifier.
During a battle, the modifier is always 2.75×, as the game defaults to that bonus being active, regardless of whether the Pokémon had previously noticed the player before initiating the battle.