This thesis presents a computational design framework for generating and exploring reticular low-carbon structures. It combines two strategies: designing resource-efficient structural forms and reusing load-bearing elements from obsolete structures. The thesis is organized in two main parts. Part I introduces a computational design framework for the exploration of diverse yet efficient structural typologies in static equilibrium, focusing on resource efficiency. The method consists of two key steps: layout and geometry. In the layout step, a new layout optimization approach is developed, leveraging sparse ground structures and dynamic node placements to generate and explore discrete structural forms. This step is formulated as a Linear Programming problem, allowing real-time computation of performance-driven, diverse layouts. In the geometry step, a new geometry optimization method refines the generated layouts. It retains static equilibrium and computes other geometric or static design goals through constraint projections and the minimization of a proximity function minimization. The geometry step also works as a stand-alone form-finding engine. Together, layout and geometry step form a powerful framework for designing efficient structural forms in static equilibrium. This framework has the potential to generate unknown yet efficient structural typologies in both 2D and 3D, setting it apart from existing tools. Part II introduces a design method for the stock-constrained design of structures, focusing on reusing structural elements over multiple service cycles. The computational tool Phoenix3D is developed to optimize the assignment of reclaimed elements to new designs, minimizing the embodied carbon of the resulting structures. Eventually, Parts I and II are implemented into a unified design framework for the Rhino/Grasshopper environment, combining both strategies to create a fast, flexible and interactive approach for designing low-carbon structures. In summary, this dissertation provides a computational design framework that combines the exploration of diverse, efficient structural forms with stock-constrained design. This equips designers with real-time computational support when designing low-carbon structures.