Before revision: 16\log{n}{nps^2}} . We improve their condition to \beta\geq\max 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}} . However, when p=O \sqrt{{\log n/{ns^2}}} , our improved condition still requires that \beta must increase inversely proportional to np.
After revision: 16\log{n}{nps^2}}  30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}} . However, when p=O \sqrt{{\log n/{ns^2}}} , our improved condition still requires that \beta must increase inversely proportional to np.