Does anyone know of a good method for finding a lower bound of the Hausdorff dimension of a set $G$?

The only method I could find is to find an $alpha$-holder function $f \colon G \to H$ then $\dim_H(G) \geq \alpha \dim_H(im(f))$. Choosing $f$ cleverly will mean that $im(f)$ will be a set whose Hausdorff dimension is already known (or at least a lower bound for it is known).

Does anyone know of a good method for finding a lower bound of the Hausdorff dimension of a set $G$?

The only method I could find is to find an $\alpha$-Hölder function $f \colon G \to H$ then $\dim_H(G) \geq \alpha \dim_H(\operatorname{im}(f))$. Choosing $f$ cleverly will mean that $\operatorname{im}(f)$ will be a set whose Hausdorff dimension is already known (or at least a lower bound for it is known).