Based on the abovementioned TPSLE algorithm, the sampling points illustrated in Figure 6 in two-dimensional space with size 64 x 2 are generated, compared with the sampling points produced by SLE and LHSD which are shown in Figure 3.
In this work, LHSD function in MATLAB and SLE algorithm  are used to make a comparison with TPSLE algorithm.
Various sampling designs are generated by three different Latin hypercube design methods including TPSLE, LHSD, and SLE.
According to the comparison study with SLE algorithm and LHSD function with various number of points in two-dimension in Table 1, the most mean values of [CL.sub.2], [[phi].sub.p], and U of the sampling designs produced by TPSLE algorithm are smaller than LHSD function, and the mean values of [d.sub.min] of sampling designs produced by TPSLE algorithm are all larger than LHSD function, which demonstrate that sampling designs using TPSLE algorithm have better performance compared with LHSD function.
For the sake of reflecting good performance of TPSLE further, the test criteria [d.sub.min], [[phi].sub.p], and U of TPSLE are studied to compare with LHSD in high dimension, as shown in Table 3.
In a word, we can conclude that better space-filling and projective properties can be obtained by TPSLE through comparison with LHSD and SLE under different criteria of [d.sub.min], [CL.sub.2], [[phi].sub.p], and U.
In this section, an illustrative comparison among our proposed TPSLE algorithm, LHSD function in MATLAB, and SLE algorithm presented in Zhu et al.
For the sampling designs with size 32 x 6 and 256 x 8, TPSLE is even more effective than LHSD. When sampling dimension n [greater than or equal to] 10, the computational time increases rapidly but is still acceptable.
In this paper, five widely accepted mathematical examples are employed to test the accuracy of metamodels that are built with different sampling methods, that is, LHSD and TPSLE.
From the results shown in Table 5, it is found that values of both NRMSE and NMAX by TPSLE algorithm are smaller comparable to those of LHSD function.
For comparison, sampling design method LHSD function is also employed.