A Suggestion for testing for the Virus

I just heard by accident the daily campaign rally by the orange monster. He emphasized that "we" had done over 1 million tests for the virus. First of all I really do not believe anything he says. Second, one million out of a country of 327 million people is not very statistically meaningful. 

It suddenly hit me what can be done. It is so simple, First divide the entire country into a small number of random lots. Then test every single person in those lots. If this is feasible then scale up and do a larger number of randomly chosen lots. The statisticians and people who do the virus infection modeling will be very excited to finally have sufficient meaningful data. They do not have to test the entire country, just a sufficient number of lots of the same size and they can scale up. Of course the choice of lots must avoid totally uninhabited regions, but otherwise random.

You see - if they get enough numbers of people infected, uninfected and infected with symptoms, and of course the people who died from the virus infection - then the analysis should be essentially the same as doing the entire country!

Note added 4/18/2020
I now feel that my proposal was very naive. The distribution of people in the US is not 2 dimensional but is 3 dimensional. The suggestion did not take into account large cities with multistory apartments and hotels. It is not obvious just how to handle these situations. For example one could define a "lot" as being a  vertical slice through a multistory structure or simply one floor and one apartment. In any case the proposal was not well thought out.