Simmer ginger in 2 quarts water until ginger pieces are completely soft. Remove ginger and chop into smaller pieces, cutting off any skin or blemishes. Return ginger to pan and bring to boil. Turn off heat and let steep at least 1 hour or up to 12 - the longer the ginger steeps the hotter the beverage will be.Strain the ginger out of the water with a cheesecloth or fine sieve. Return the water to the pan and add sugar, stirring to dissolve. Bring to a boil and cook until liquid is reduced to about 1 cup. Remove and cool. Syrup can be stored in the fridge, tightly covered, for a few days.To make the syrup into a beverage, pour 1 quart seltzer water into a pitcher and stir in syrup. Squeeze in lime juice to taste. Pour over ice and serve.