I recently found this paper eprint which estimates security of LWE instantiations using an improved Dual attack. However, I got confused looking at their example in this site. For example, in the case of NewHope their example gives states that minimum operation (rop) using dual attack is $2^{371}$, whereas the minimum $\beta$ is $1168$. So following the NewHope paper the securty of NewHope should be $2^{.2075*1168}\ =\ 2^{242}$. Which indeed increases the security of the NewHope. I am wondering which should I take as the bit security?
Another question is definition of $\alpha$, in their paper they define $\alpha=\sigma*\sqrt{2\cdot \pi}/q$ whereas in the example they have taken $\alpha=\sigma^2/q$ (NewHope parameter).