Make the ginger syrup:
Peel and chop ginger. After peeling and chopping you'll be left with roughly 1 1/2 pounds of peeled ginger. If it's more or less, it's not a big deal
Place the chopped ginger and water in a blender or a food processor. Blend or process until mostly smooth. Transfer the blended ginger into a large pot and add the sugar. Stir to combine.
Bring to a boil over high heat, then reduce the heat to low and simmer for about 15-20 minutes until slightly reduced and syrupy.Remove from heat and allow it to come to room temperature. Strain the mixture, pressing down on the solids to extract as much liquid as possible. Discard the solids and transfer the syrup to a large glass jar or bottle with a tightly fitting lid. Makes about 5 1/2 cups of ginger syrup.
Make the ginger lime soda
Spoon 2-3 tablespoons of ginger syrup to a tall glass. Add the lime wedges and muddle limes with a muddler or back of a wooden spoon until limes have released their juice. Add ice and top with seltzer. Stir briefly to combine and enjoy.