Fano threefolds in positive characteristic II

Let $X$ be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that $\mathrm{\mid }-K_X\mathrm{\mid }$ is very ample and each of the index and the Picard number is equal to one. We prove that $3\le g\le 12$ and $g\mathrm{\ne }11$ for the genus $g$ of $X$. Moreover, we show that there exists no smooth curve on $X$ along which the blowup is Fano.