Combine strawberries, sugar, and water in a medium saucepan and bring to a simmer over medium heat, stirring until the sugar dissolves.

Reduce heat to low and simmer for 10 minutes, or until the strawberries have softened and released their juices, then remove from heat and let cool slightly.

Strain the mixture through a fine-mesh sieve into a clean bowl, pressing on the solids to extract all the juice, then discard the solids and let the syrup cool completely to room temperature, then chill in the refrigerator.

In a large pitcher, combine the chilled strawberry syrup and fresh lime juice, stirring well.

To serve, fill glasses with ice, pour in about 1/4 to 1/3 cup of the strawberry-lime mixture, and top with cold sparkling water or club soda, adjusting to taste.

Garnish each glass with fresh strawberry slices and lime wedges before serving immediately.