accessible digitized national sampling frame for the country. The boundaries of the PSUs and other administrative units in our sampling frame offer several benefits. For example, it helps to avoid potential mistakes of households outside of the selected to be listed and covered in the survey data. If this potential mistake is not random, it might severely undermine the quality of the subsequent analysis using the collected data. However, this error could be non-random and more systematic as this mistake can be more frequently made for PSUs with larger areas and thus longer boundaries. So, this feature could play a critical role from the quality control perspective.<sup>23</sup> It may be challenging to directly compare the resources and budget of our automatic method to manual approaches because many countries do not release a breakdown of the costs associated with conducting censuses at different phases, especially when it comes to the resources needed to manually digitize national census enumeration areas. For example, the 2010 census mapping effort in Zambia was projected to cost US $7 million and take almost two years to complete (United Nations Secretariat, 2007). If the pre-census sample frame in Armenia had been digitalized manually, we would have needed to dedicate significant financial resources to the extensive training of a team of cartographers to teach them how to digitize all the units on high-resolution satellite imagery. In addition, all pre-enumeration areas were to be manually digitized by the team according to all specified requirements. It would have taken a lot of work to verify quality and correct several geometric errors because this was hand-drawn. The entire procedure is obviously time- and resourceconsuming. Nonetheless, it took less than two months to complete the automatic creation of the pre-census sampling frame in Armenia, including the manual correction required due to a lack of spatial input data. One specialist carried out the entire procedure. The significant labor, time, and cost savings achieved by developing an automatic pre-census sample frame could be invested in various aspects of national surveys and census preparation.

Despite limitations, the method was successfully implemented, and a national sampling frame was produced for Armenia. From financial, timeframe, and technological perspectives, the method performed better than the conventional manual techniques. Delineating a nationwide sampling frame by hand has historically required years and massive financial resources. In addition, the manual method is prone to several geometric issues, including gaps, overlaps, pockets, and disjoints since it is carried out by humans. These geometric problems could lead to bias being introduced into the frame and eventually into the collected data. Nevertheless, there are no geometric problems with the automatic method. This approach has several benefits over the gridded population sampling frame. Several researchers have directly employed gridded population data as a sample frame (Thomson et al., 2017; Cajka et al., 2018; Qader et al., 2020). The design of the sampling units is the primary distinction between our approach and the gridded population sampling frame. Houses and other structures are cut because the grid’s outline is not in line with features that can be seen on the ground. In contrast, the preEA tool creates pre-EA boundaries that adhere to observable elements like natural borders and roads.

> 23 A digital map of the enumeration areas also provides a significant amount of spatial information, such as settlement areas with residents within the PSU and their centroids, which can be used, for example, as starting points for random walks. If the household listing is possible for each pre-EA and all household addresses are available, a random walk procedure and thus starting point information are unnecessary. However, complete household listing is not available or hard to obtain in some developing countries, and the household listing operation—visiting each of the selected PSUs and listing all residential households in those PSUs—is costly and time-consuming. So, although not encouraged, some surveys employ random walks as a last resort to select households in the second stage if subject to pressing constraints, and thus, the digital map supports such a procedure.

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