Exact proportions of sugar to water in sorbet
I don't have a recipe for a sorbet without any fruit contributing sugar, but I do have something very close: the lemon sorbet from The Perfect Scoop. It uses a cup of lemon juice, which contains only 6 g of sugar, along with 2.5 cups of water and 1 cup of sugar.

So 3.5 cups (828 mL) of water with 1 cup (200 g) of sugar should be good, or a ratio of 4:1 by weight.