In a saucepan on medium heat, combine sugar and water, stirring until the sugar is dissolved. Add the sliced ginger and bring the syrup to a light boil. Cover, reduce heat, and allow to simmer for about 15 minutes. Strain out the ginger and bottle under a tight seal. The ginger syrup can be stored in the refrigerator for two weeks. In a cocktail shaker muddle the Thai basil and blueberries. Add vodka, lemon juice, and 3/4 oz. ginger syrup and shake. Pour into a Collins glass, top with soda water, and serve.