I have the Trans-Temporal Array, and I was wondering what tech level you need for the highest level Base defense module.

It's tied to your ship research. If for example, like me, your guns stop at Singularity Launchers (my research is more defense-focused for now) then all you can build is the Singularity Turret. Which isn't to say someone else in your legion with better guns can't strap them on instead though. There's also a rank limit, you need to have your legion base up to a minimum level for some tech. The Sungularity Turrets are a Base Rank 3 unlock

I know all of that; I wanted to know which level of Defense research unlocks the highest level Base Defense structure.

You need to have the last tier of defenses researched, trans-entropy fields.

Alright, thanks for the information.