Modifications of the Bekenstein bound from dimensional reduction of covariant entropy bound

We consider dimensional reduction of the covariant entropy bound from D + S-1 dimensional geometry of M x S-1 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 local Bekenstein bound from the D dimensional view point. With this new local Bekenstein bound, it is possible to saturate the lightlike holography bound 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.