I'd like to see a Star Trek system that went arcology style from this video, with a population of ~1 trillion:
https://www.youtube.com/watch?v=TqKQ94DtS54 (~17 minutes)
Short version:
Key requirements are cheap construction, compact high-efficiency power supply, and advanced robotics
Controlled light, humidity, and nutrient content allow greenhouses to produce lots of food
Need to solve the Elevator conundrum (where taller buildings need more surface area devoted to elevators)
Example Arcology
100 stories tall, 800 feet wide cylinder, 10,000 square feet per person (including living space, farms, malls, elevators, etc), 50 feet-stories of outside window per person, unless you need the outside surface for growing more food (grape vines for curtains?
Each will have a population of ~5000 (Dunbar's number)
Figure one of these every 2-3 miles of coastline to allow for water cooling, and the rest of the continental interior is left natural.
First Contact:
Fed Diplomat: "Welcome to the Federation, we are a multi-species interstellar government with 1 trillion members."
"Hi, we're Gatharis, a single planet with 1 Trillion people"
Fed Diplomat: