  Group testing allows saving chemical reagents, analysis time, and costs, by
testing pools of samples instead of individual samples. We introduce a class of
group testing protocols with small dilution, suited to operate even at high
prevalence ($5\%-10\%$), and maximizing the fraction of samples classified
positive/negative within the first round of tests. Precisely, if the tested
group has exactly one positive sample then the protocols identify it without
further individual tests. The protocols also detect the presence of two or more
positives in the group, in which case a second round could be applied to
identify the positive individuals. With a prevalence of $5\%$ and maximum
dilution 6, with 100 tests we classify 242 individuals, $92\%$ of them in one
round and $8\%$ requiring a second individual test. In comparison, the
Dorfman's scheme can test 229 individuals with 100 tests, with a second round
for $18.5\%$ of the individuals.
