Hmm, in one game I'm playing earth has 15 dsts with strength of 4500, which can detect a strength 100 thermal contact (one of my fighters which goes 10,000 km/s) at a range of 450 million kilometers, also none of my fighters have any em emissions.
Now, if you needed to detect such a contact as far out as Neptune you would need 4.5 billion kilometers range, which would require a strength 4.5 million dsts, which with my technology would need 15,000 dsts.
You'll need 2,250,000 Duranium and Uridium to build them, but on the bright side they require no population to operate.