## 3 Results  
### Analysis of the Influence of Super-Grid Size for the Proposed Sampling Design Method  
Since the sample size was restricted by resources, including field labor, soil physicochemical analysis, and funding, this paper proposed a new sampling design method that recognized representative sample locations to improve soil mapping accuracy for a limited sample size (i.e., 36 sampling points in this paper). This method determined the appropriate super-grid size and then assigned the limited sampling points to the super-grids based on the remote sensing data to identify the representative sample locations. As discussed in Section 2.2.1, this paper compared super-grid sizes of \(200\times 200\) m\({}^{2}\), \(300\times 300\) m\({}^{2}\), \(400\times 400\) m\({}^{2}\), \(500\times 500\) m\({}^{2}\), \(600\times 600\) m\({}^{2}\), and \(700\times 700\) m\({}^{2}\) and analyzed their soil mapping accuracy. Table 3 shows the numbers of the candidate samples, the diversity indexes, and the number of sampling points of different sized super-grids. Different super-grid sizes resulted in various DIs and numbers of sampling points within one super-grid. For the \(200\times 200\) m\({}^{2}\) super-grid, super-grids 6, 9, and 10 had relatively higher DIs than the others. The number of samples ranged from 1 to 3, and super-grids 6 and 10 had the most samples. For the \(300\times 300\) m\({}^{2}\) super-grid, super-grids 2, 4, and 5 had higher DIs and more samples than the others. The number of samples ranged from 1 to 5. For the \(400\times 400\) m\({}^{2}\) super-grid, the DIs of super-grids 1 and 3 were relatively higher. Additionally, they had more sampling points. The number of samples varied from 4 to 9. For the \(500\times 500\) m\({}^{2}\) super-grid, the super-grids 1 and 3 had higher DIs and a higher number of sampling points compared to the other super-grid IDs. The number of sampling points was from 1 to 13. For the \(600\times 600\) m\({}^{2}\) super-grid, super-grid 1 had the highest soil variation, indicated by the highest DI. The number of samples ranged from 2 to 18. For the \(700\times 700\) m\({}^{2}\) super-grid, super-grid 1 had relatively higher DIs and the largest area, and thus, its number of sampling points was more compared to the other IDs. The number of sampling points ranged from 1 to 23. As the super-grid size increased, the difference in the number of sampling points between the super-grids increased. It indicated that the spatial coverage gradually worsened, whereas the feature space coverage improved as the super-grid size increased. By calculating the sum of the numbers of sampling points for all super-grids, the numbers of sampling points within the farm field using super-grids that ranged from 200 to 700 m were 37, 37, 35, 37, and 36, respectively. The reason that some calculated sample sizes were not equal to the given limited sample size (i.e., 36 sampling points) was that the sampling number in each super-grid, as calculated by Equation (4) may not be an integer. According to Section 2.2.2, 36 sampling points were randomly chosen from the sampling design results that were produced by the \(200\times 200\) m\({}^{2}\), \(300\times 300\) m\({}^{2}\), \(500\times 500\) m\({}^{2}\), and \(600\times 600\) m\({}^{2}\) super-grids after determination of the sampling locations. For the \(400\times 400\) m\({}^{2}\) super-grid, super-grid 1 added one sampling point. Finally, the sample locations within each super-grid were determined based on the rule described in Section 2.2.3. Figure 4 shows the clustering results based on the crop yield information and the distribution of the sampling points. The distribution of the sampling points of the \(200\times 200\) m\({}^{2}\) super-grid provided better spatial coverage compared to distributions of other different sized super-grids. As the super-grid size increased, the good spatial coverage decreased, and the environmental covariate information was given more weight to determine the sample locations.