Generating the mapping class group of a punctured surface by involutions

Let Σ_{g, b} denote a closed oriented surface of genus g with b punctures and let Mod(Σ_{g, b}) denote its mapping class group. Kassabov showed that Mod(Σ_{g, b}) is generated by 4 involutions if g > 7 or g = 7 and b is even, 5 involutions if g > 5 or g = 5 and b is even, and 6 involutions if g > 3 or g = 3 and b is even. We proved that Mod(Σ_{g, b}) is generated by 4 involutions if g = 7 and b is odd, and 5 involutions if g = 5 and b is odd.