There's a lovely article on the high-pop world of Azun in JTAS17 (?); it
serves as an admirable introduction to the theory of the arcology, a city
that accomplishes maximum pop. density, minimum environmental impact, and
maximized human comfort all in one swoop. Suffice it to say that based
on the theories of Paolo Soleri, who developed the idea of the arcology in
the 1960s, 10 million people in a three-klick square is not only possible
but in fact quite easy.
I use arcological theory (straight from Soleri, not the watered-down stuff
the popular media tends to handle) in the games rules sets that I write;
if your local library has a copy of "Arcology: The city in the Image of Man"
by Soleri, I heartily recommend reading it, assuming they'll let you take it
out. (It's a very unusually-designed book, and most public libraries consider
it a work of art as well as a reference and hence limit its circulation).
A very, VERY poor substitute is Niven and Pournelle's "Oath of Fealty,"
which gleefully manages to drag every bit of Soleri's vision through the
dung heap. Feh!
I should also point out that high technology makes arcological building
easier, but it is by no means vital: any TL above 4 could build arcologies,
with the maximum population density growing as the tech level did. The
arcology is a philosophy of architecture, not a specific machine; arcologies
can have only a few hundred people, or millions.
I can go into more details if people want me to, but not immediately; I'm
leaving tomorrow for a research trip, and will have only limited net access
from now until June 30th or July 1st.
metlay