Which is the most efficient irrigation system?

Buried drip irrigation system is the most efficient. Irrigation efficiency (IE) is defined as the amount of water stored in the root zone of the crop for later use divided by the amount of water that provided to the field. Typically surface irrigation is the least efficient, followed by sprinkle, and drip and trickle irrigation is the most efficient type of system. It is not easy to calculate efficiency, in the field so typically we get numbers for IE from the literature. Those number derived after scientific research.

You can find values for IE from:
FAO paper24 Water requirements (1977), table 37
www.fao.org/3/a-f2430e.pdf

FAO Handbook Pressurised Irrigation (2007), table 6.7
www.fao.org/3/a1336e/a1336e00.htm