Great puzzle. Bear in mind the asymmetry between false positives and false negatives in this case. For false positives (positive result but not actually carrying the virus) we recommend that they self-isolate for two weeks and monitor symptoms. They lose two weeks of freedom of movement/interaction, but are otherwise unharmed (and relatively protected from new infections during this period). A false negative, on the other hand, can go on to infect other people, even if they remain asymptomatic. Some of the people downstream in the infection chain may be seriously harmed AND the epidemic is prolonged.
Pre-print of the paper with details of the methods, etc: https://www.medrxiv.org/content/10.1101/2020.03.26.20039438v1.full.pdf
Similar methodology, but with pools of 10:
https://www.medrxiv.org/content/10.1101/2020.03.30.20043513v1.full.pdf
Peer-reviewed paper with pools of up to 96 samples for avian influenza:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2878216/
None of this is surprising given that...
1) The threshold for detecting the (very similar) SARS virus was 37~4000 copies per mL (depending on the platform -- this suggests that choice of platform will be critical for this to work well) https://jcm.asm.org/content/42/5/2094
2) Patients with COVID-19 generally have 10,000 to 1,000,000 copies per swab. Not sure how many mL per swab, but not many I suspect: https://www.nature.com/articles/s41586-020-2196-x_reference.pdf
3) PCR uses primers to selectively amplify only the target RNA. The presence of other RNA is not really a problem
...
Put it all together and here is the argument: https://www.medrxiv.org/content/10.1101/2020.03.27.20043968v1.full.pdf