What system did Han rulers use to build the most effective bureaucracy?

Han rulers established an effective bureaucracy through the implementation of a merit-based civil service examination system. This allowed for the selection of officials based on their abilities and knowledge rather than aristocratic birthright. Additionally, the Han dynasty emphasized the importance of Confucianism, which promoted values such as education, moral integrity, and governance for the people. This combination helped create a more efficient and responsive administrative system that supported the expansion and stability of the empire.