  This article provides new lower bounds for both Schur and weak Schur numbers
by exploiting a "template"-based approach. The concept of "template" is also
generalized to weak Schur numbers. Finding new templates leads to explicit
partitions improving lower bounds as well as the growth rate for Schur numbers,
weak Schur numbers, and multicolor Ramsey numbers $R_n(3)$. The new lower
bounds include $S(9) \geq 17\,803$, $S(10) \geq 60\,948$, $\mathit{WS}(6) \geq
646$, $\mathit{WS}(9) \geq 22\,536$ and $\mathit{WS}(10) \geq 71\,256$.
