What it the optimal number of construction sites for the various modes?

It depends a little on your strategy but mostly on your land goals.

For maximal turn efficiency with all CS built right away:
Opti_BPT= (Land_Goal/4*Govt_BPT_Multiplier)^0.5

So for Normal govt Optimal BPT is
10000 acres --> 50
20000 acres --> ~71
40000 acres --> 100
200000 acres --> ~224

So for Theocracy Optimal BPT is
10000 acres --> ~59
20000 acres --> ~84
40000 acres --> ~118
200000 acres --> ~265

Dict is lower, with more CS. Don't play Dict, be a netter.

Ohh, and I forgot to mention switches and the fact that you usually build some buildings before you reach your BPT goal.

So if you switch the at one point instead use the total amount of buildings you plan to build during the reset. Therefore the optimal BPT is higher.

And if you build buildings before reaching your BPT goal, because you have to get income before perhaps, this would mean that your optimal BPT is a bit lower than what this formula yeilds.

I always try to get min of 50 BPT which = 180 constructions sites

Get to 400-550 acres before OOP BPT is ~ 35 at that point doing CS startup, once OOP explore to 1k or hit to 1k then get 50 - 55 BPT then grow to 5k and once there build your BPT upto 75-80 and grow it 5 a day until you reach your goal.

:)

1

Regardless of strat I almost always get to 80 CS by turn 99. If you're going to be converting your strat at some point, for instance a tech start, factor in the acreage you need to rebuild after tearing down. As Gerdler said, divide your goal acreage by 4, then take the square root of that.