  We performed lattice Landau gauge QCD simulation on \beta=6.0, 16^4, 24^4,
32^4 and \beta=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that
minimizes the norm of the gauge field, and measured the running coupling by
using the gluon propagator and the ghost propagator. In view of ambiguity in
the vertex renormalization factor \tilde Z_1 in the lattice, we adjust the
normalization of the running coupling by the perturbative QCD results near the
highest momentum point. It has a maximum \alpha_s(q)~ 2.1(3) at around q=0.5
GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached
-0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is
\alpha_G=0.20 but there is an exceptional Gribov copy with \alpha_G=0.27. The
features of the exceptional Gribov copy are investigated by measuring four
one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to
each lattice axis. We observe, in general, correlation between absolute value
of the Kugo-Ojima parameter and the degree of reflection positivity violation
in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov
copy has an axis whose gluon propagator manifestly violates reflection
positivity, and the average of the Cartan subalgebra components of the
Kugo-Ojima parameter along this axis is consistent to -1. The running coupling
of the enemble average shows a suppression at 0 momentum, but when the ghost
propagator of the exceptional Gribov copy is adopted, the suppression
disappears and the data implies presence of the infrared fixed point
\alpha_s(0)~ 2.5(5) and \kappa=0.5 suggested by the Dyson-Schwinger approach in
the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and
N_f=2 unquenched SU(3) QCD are also made.
