Can Homebrew run on 3.1 Wii menu

Can you install Homebrew and required apps on Wii menu 3.1?

Secondly, why is 3.2e regarded as the best wii menu? is there an easy way to upgrade to 3.2, i know how to downgrade but not upgrade.

Thanks in advance.

Yes, I installed the HBC myself on 3.1 3.2 is the best because it was the latest firmware available before Nintendo started trying to bloack the twilight hack and the homebrew channel. You can upgrade to 3.2 using tona's anyregion changer application.

DON'T UPDATE THROUGH NINTENDO, EITHER THROUGH GAME DISCS OR INTERNET. it blocks some homebrew

^ The only "homebrew" it blocks is the stuff that runs backups and wads. Oh, and dvdx too.