variables are quenched. The QEK model might have no problem in principle, but its computational cost is larger than that of the TEK model. Although the TEK and QEK model are reduced models to a single hyper-cube, recent studies deviate from them. The contemporary method might be the partial reduction [@Narayanan:2003fc]. This work showed that the large-$N$ reduction is valid above some critical physical size $l_c$. This means that for a lattice size $L$ the reduction holds below some lattice coupling $\beta(L)$. In order to take continuum limits we should avoid the bulk transition point $\beta_c^B$, causing the condition $\beta_c^B<\beta(L)$ to be necessary. That is, there is a lower limitation for the lattice size $L_c$ for the continuum reduction. In addition, the twist prescription is also applicable to the partial reduction [@GonzalezArroyo:2005dz]. Due to the twisted boundary condition, the lower limitation $L_c$ can be reduced. Therefore, combination of the twist prescription and the partial reduction would be quite efficient in the current situation.

Note also that NCYM on fuzzy ${\mathbb R}^4$ could be realized by using TEK with quotient conditions [@Ambjorn:1999ts] which give a periodic condition to eigenvalues and hence quantum fluctuation is suppressed. Further study in this direction would 