The fastest way is to kick out the gym
Mingjiao can reach 2000+ by completing sect tasks
Chivalrous - Once your notoriety is high, it is rumored that defeating them in missions will give you a lot.
Watching the Yanjing Arena
Then complete some branches
Dog fighting on the Mongolian-Xinjiang border gives 300
Shaolin Temple Back Mountain Bronze Man branch line gives 200
Mingwang branch line gives 500
Shaoguan Dao Gentry Branch Line 200
Mao Shiba branch gives him a big sword 70
200 Number One Scholar in the Imperial Examination
Then there are the various main lines
Everyone will have some experience