  The kernel interpolant in a reproducing kernel Hilbert space is optimal in
the worst-case sense among all approximations of a function using the same set
of function values. In this paper, we compare two search criteria to construct
lattice point sets for use in lattice-based kernel approximation. The first
candidate, $\calP_n^*$, is based on the power function that appears in machine
learning literature. The second, $\calS_n^*$, is a search criterion used for
generating lattices for approximation using truncated Fourier series. We find
that the empirical difference in error between the lattices constructed using
$\calP_n^*$ and $\calS_n^*$ is marginal. The criterion $\calS_n^*$ is preferred
as it is computationally more efficient and has a proven error bound.
