Use Japanese shark skin grater to finely grate whole piece of ginger. Set aside.
Put peeled garlic into mortal and use pestle to smash them into pieces. Use a spoon to scoop them out, include the juice if any. Set aside.
In a small bowl, combine water, fish sauce, sugar, lime juice. Stir to dissolve sugar completely.
Put garlic and chopped Thai chilies in. Gradually add grated ginger, start with ¼ tsp. Adjust the amount of ginger in the dipping sauce according to your taste.
Store the sauce in an air tight container in refrigerator for up to 3 days.