Unlike Helium-3 and Mineral Ore, Antimatter can not be produced in your base by harvesting it from resource asteroids; the Antimatter Silos on your base are only storage units for the Antimatter you bring back. The main way to gain Antimatter is from certain cargo fleets. On the Planet Map you will see purple Antimatter Cargo fleets that spawn around Alien Artifacts that carry only Antimatter, and on the Sector Map any of the VEGA Cargos generally carry Antimatter along with Helium-3 and Mineral Ore. You can also consider attacking other players, and taking their Antimatter from them!
