a low - microcracked porous cordierite honeycomb ceramic particulate filter having a high strength in combination with a very low pressure drop , a very high filtration efficiency , and a high thermal shock resistance . little or no microcracking , a fine median pore diameter , and a narrow pore size distribution contribute to high strength . a thin channel wall , high wall permeability , and narrow pore size distribution , contribute to low pressure drop . a fine pore diameter and narrow pore size distribution with a minimum of coarse pores contribute to high filtration efficiency . a high strain tolerance , mor / e , contributes to high thermal shock resistance . particulate filters disclosed herein can be useful as a hot gas particulate filter , and particularly as an internal combustion engine exhaust gas particulate filter , such as an exhaust gas filter for a gasoline direct injection engine .