Which intel HD graphics are best for corei3 and windoes 8

There is only the Intel HD 3000 graphics core for all Sandy Bridge Core i3 laptop CPUs. It is equivalent to the desktop Radeon HD 5450, but it only supports DX10.

Ivy Bridge Core i3 laptop CPUs (like the i3-3110M) are not expected to be released until Q3 2012 (July - Sept.) and will have the Intel HD 4000 graphic core. It is about equal to a Radeon HD 5550 (about 40% faster than the Intel HD 3000) and it supports DX11.