This work considers estimation of dichotomous characteristics of rare populations by sample survey. In particular, we investigate optimum allocation when anetwork samplingrule (also calledmultiplicityrule) is used to link members of the rare population to enumeration units and when the enumeration units are chosen by stratified random sampling. For this situation, formulas are derived for optimum allocation under the restriction that an enumeration unit is linked to at most one member of the rare population, and the cost efficiency of network sampling rules is compared to that of conventional enumeration rules.