In the early phases, random testing to estimate what proportion of the population are infected is prohibitively expensive - you'd need to test hundreds of thousands to find just a few infected.
In the later phases, you want to know who has been infected, yet the commonly available test in fact measures who is currently infected (ie. It can't detect those who are still liable to get infected, which is what you need for good modelling).
Antibody tests which are being prototyped by many groups should fill this need.
Even testing 100 people would still be informative and give you an upper and lower bounds on the number infected. You don't need an exact number to form policy.
We can only test for active infections, not past infections. The disease is still rare enough to not allow for sparse testing but common and infectious enough to spread quickly. The disease is still not fully known. The disease can take up to (or longer) than 14 days to show the symptoms to show that we should test a person. The disease can spread from non-symptomatic persons.
Can't you see how these factors mean that testing 100 people would not lead to a proper representative sample?
I don't think 100 people would be enough to properly and statistically test for a common cold, much less for a disease like this.
In the later phases, you want to know who has been infected, yet the commonly available test in fact measures who is currently infected (ie. It can't detect those who are still liable to get infected, which is what you need for good modelling).
Antibody tests which are being prototyped by many groups should fill this need.