How many animals must be tested from within a group (herd) to determine that the group is free from infection?

These calculations asume that if the infection is present at all, then at least certain proportion of individuals are expected to be infected. Given strong a priori evidence that the prevalence of disease (if present) will meet or exceed the inputted true prevalence, then if no animals react positively, the inference can be made that the herd is free of infection. Caveat: few tests are perfectly specific; therefore, positive test results should be confirmed before concluding infection does exist within a herd.