1.Combine sugar and water in a small saucepan. Add ginger to pan; stir over medium heat, without boiling, until sugar dissolves. Bring to the boil; boil for 5 minutes. Transfer to a heatproof jug; cool. Add lime juice and vodka to jug; cover and refrigerate until ready to use.
2.Pour 2 tablespoons of the ginger vodka mixture into 8 chilled glasses; add a couple of pieces of the cooked ginger and a few slices of lime.
3.Just before serving, fill glasses with two 750ml bottles of chilled sparkling wine. Serve cocktail with oysters on a bed of ice.