Mix 8 cups water, 2 1/2 cups sugar and 1/2 cup chopped fresh ginger in a heavy pan over medium heat; stir until sugar has dissolved. Bring to a boil, then reduce heat to low and simmer for 5 minutes. Cool completely; strain. In a large pitcher combine sugar syrup, 2 cups fresh lime juice and 4 cups chilled ginger ale. Serve over ice.