2 problems

Optimality conjecture. There exists a constant $s_q$ such that whenever $s\in[-1,s_q)\cap T_n$, the refinements described above are the best bounds that can be obtained from Theore…

Let $q>2$ and let $\theta=1-1/q$. For $x$ in the relevant relative-distance range, write $\alpha(x)=\lim_{n\to\infty}n^{-1}\log_q A_q(n,xn)$, where $A_q(n,d)$ is the maximum size o…