Generating the mapping class groups by torsions

Let S-g be a closed oriented surface of genus g and let Mod(S-g) be the mapping class group. When the genus is at least 3, Mod(S-g) can be generated by torsion elements. We prove the following results: For g >= 4, Mod(S-g) can be generated by four torsion elements. Three generators are involutions and the fourth one is an order three element. Mod(S-3) can be generated by five torsion elements. Four generators are involutions and the fifth one is an order three element.