  We consider dimensional reduction of the lightlike holography of the
covariant entropy bound from D+1 dimensional geometry of M X S to the D
dimensional geometry M. With a warping factor, the local Bekenstein bound in
D+1 dimensions leads to a more refined form of the bound from the D dimensional
view point. With this new local Bekenstein bound, it is quite possible to
saturate the lightlike holography even with nonvanishing expansion rate. With a
Kaluza-Klein gauge field, the dimensional reduction implies a stronger bound
where the energy momentum tensor contribution is replaced by the energy
momentum tensor with the electromagnetic contribution subtracted.
