Random Population Sampling!

CDC and/or state governments need to test random individuals (population representative sampling) for the current  infection and/or antibodies. Antibodies are indication of prior infection and immunity.

Sampling allows comprehensive testing of the whole nation using less than 100,000 tests, about a third of the number of tests that are currently performed daily. Because most tests are currently performed selectively, mostly on people with strong symptoms, they are useless for statistical purposes.

Explanation for politicians: this works like political polling, except that it cannot be done remotely.