High tech in outbreak is the best bet, but the usual caveats apply:
- After jumping into system, verify on the system map that the controlling faction is actually in state outbreak. The status in the galaxy map is sometimes wrong.
- Higher population systems offer better chances than lower population systems.
- You need to reach deep space, and systems with multiple stars have their deep space much further out than single star systems. If you have a choice, use a single star system.
- The materials that are in a HGE are partially dependent on allegiance. If you are in a federal system, HGE can spawn core dynamics composites in addition to or instead of PI. In an imperial system, imperial shielding. Using an alliance or independent system improves your chances.
But in the end, it comes down to RNG luck.