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It has been widely reported that the jamming transition point phi_J is not uniquely determined but shows protocol dependence.Whereas phi_J is obtained around 65% in three dimensions by compressing a dilute hard sphere fluid,higher value of phi_J is attained when a dense thermally equilibrated fluid is compressed.Recently, we develop a very efficient thermalization setting of a hard sphere system which is composed of continuous polydispersity of the particle diameters and a non-local swap Monte-Carlo algorithm.This method enabled us to thermalize the hard sphere fluid up to nearly 66%, which is beyond phi_J of the system obtained by the compression of dilute states.By compressing these high density equilibrium fluids, we obtain an unprecedentedly wide range of phi_J, so-called J-line, from around 65% to almost 70%.These denser phi_J states also have on average 6 contact number per particle (isostaticity).Also, the power law singularity near contact in the radial distribution function is observed over the entire J-line with a fixed exponent whose value is consistent with the prediction of the mean-field theory. Furthermore, we examine local and global structural properties of high density jammed states.Even though the isostaticity and critical behavior are preserved over the entire J-line, the high density jammed states show qualitatively distinct structural properties compared to the lowest jamming transition point, phi_J = 65%, which has been widely studied in the past.Especially, we demonstrate the following local and global structural properties.Growing local order:Even though our jammed configurations are all isostatic, they do differ at the local structure level.We reveal this by a combination of bond-orientational order analysis and Voronoi tessellation.This analysis detects growing icosahedral order with increasing phi_J and shows no signs of crystallization in our configurations.Disturbing the hyperuniformity: Hyperuniformity, which corresponds to vanishing of the density (or volume fraction) fluctuations at long wavelengths is believed to be one of the characteristic properties of the jamming transition point.We analyze the two body correlation function of the volume fraction to examine the hyperuniformity in our system.We observe excitations at small wavenumbers which disturb the hyperunifromity at the high density jammed states.Also, these excitations increase with increasing phi_J.Suppression of the finite size effect: It has been argued that the jamming transition is a phase transition which occurs at the thermodynamic limit.Also, several length scales diverging at phi_J are well characterized as a consequences of the isostaticity of the system.However, the length scale which causes finite size effects at the jamming transition is not yet understood. We study finite size effects for two protocols, compression of dilute and of dense fluids.Interestingly, we find that finite size effects are significantly suppressed by the protocol using compression of the dense fluid.This observation implies that the length scale causing finite size effects is not related to the isostaticity of the system.Instead we discuss the mechanism of the finite size effect of the jamming transition using an analogy with the potential energy landscape thermal systems.