Before revision:  Here we show that independent of the total size of population with frequent interactions among its members, about 15000 tests with randomly selected people per day  suffice to obtain valuable data about the current number of infections and their evolution in time . In contrast to testing confined to particular subpopulations such as those displaying symptoms, this will allow close to real-time assessment of the quantitative effect of restrictive measures.
After revision:  Here we show that independent of the total size of population with frequent interactions among its members, about 15000 tests with randomly selected people per day suffice to obtain valuable data about the current number of infections and their evolution in time , thus enabling close to real-time assessment of the quantitative effect of restrictive measures.