The authors consider the optimal zero-padding factor of the kernel truncation method (KTM) in the convolution-type nonlocal potential evaluation, and strictly show that the optimal zero-padding factor is \(\sqrt{d} + 1\), \(d\) being the space dimension. The memory costs are significantly reduced to a small fraction, i.e., \(\left(\frac{\sqrt{d}+1}{4}\right)^d\), of that in the fourfold algorithm. The authors deduce that twofold padding is optimal for the one-dimensional problem, whereas threefold padding is sufficient to get spectral accuracy for the two- and three-dimensional problems. For the anisotropic density, the total optimal zero-padding factor grows linearly with the anisotropy strength. The KTM is obtained by the Fourier spectral method, and it can be rewritten as a discrete convolution regardless of the anisotropy strength. Providing that the discrete tensor is available through a precomputation step, the effective computation is simply a pair of fast Fourier transform (FFT) and inverse FFT (iFFT) on a double-sized density. Error estimates are provided for both the nonlocal potential and the density in \(d\) dimensions. Several numerical experiments are carried out to confirm the enhancements in terms of memory and computational cost.