  We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70,
3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number
$Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave
vector set method (introduced earlier) to approximately solve the Navier-Stokes
equation. First, also for these extremely high Reynolds numbers $Re_\lambda$,
the energy spectra as well as the higher moments -- when scaled by the spectral
intensity at the wave number $k_p$ of peak dissipation -- can be described by
{\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR
scaling exponents $\zeta_m$ of this universal function are in agreement with
the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the
$Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to
slight energy pileup in the spectra, as in the experimental data (bottleneck
phenomenon).
