Cook ginger in water in a small saucepan at a low simmer, partially covered, 45 minutes.
Remove from heat and let steep, covered, 20 minutes.
Strain mixture through a sieve into a bowl, pressing on ginger and then discarding. Return liquid to saucepan and add sugar and a pinch of salt, then heat over medium heat, stirring, until sugar has dissolved. Chill syrup in a covered jar until cold.
Mix ginger syrup with seltzer and lime juice (start with 1/4 cup syrup and 1 1/2 teaspoons lime juice per 3/4 cup seltzer, then adjust to taste).
