To overcome the traditional drawbacks of chain sampling (respondent-driven sampling) methods, a team from the University of North Carolina developed a sampling method known as "network sampling with memory." Its unique feature is to recreate, gradually in the field, a frame for the target population composed of individuals identified by respondents and to randomly draw future respondents from this frame, thereby minimizing selection bias. The algorithm includes an initial exploratory or "Search" phase that looks for new network segments, followed by a phase of random draws within the new network. Used for the first time in France between September 2020 and June 2021 for a survey of Chinese immigrants in Ile-de-France (ChIPRe), implementing the method was extremely difficult. Specifically, we discovered a paradox inherent in the "Search" algorithm: it shows a "preference" for small rosters (those with few referrals), which were considered as an opportunity to explore unexplored parts of the network, as opposed to large rosters that comprise more people already referred (duplicates) and associated with parts of the network that have already been explored. As a result, the efforts of "good" surveyors were not always rewarded with selection of the rosters they had collected after time-consuming negotiations in the field (future questionnaire potential, which meant that their remuneration depended on this random draw). In all, 501 questionnaires and 1,698 referrals were collected.