NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets

A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of $NPT(NP\cap P/poly)$. In this paper, we show that $NE\not\subseteq NP(NP \cap$ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c>0,$|A^{\le n}|\le 2^{nc}$ for infinitely many integers n). Our result implies $NE\not\subseteq NPT({pad(NP, g(n))})$ for every time constructible super-polynomial function g(n) such as $g(n)=n^{{\ceiling{\log\ceiling{\log} n}}}$, where Pad(NP, g(n)) is class of all languages $LB={s10^{{g(|s|)-|s|-1}:s\in} B}$ for $B\in NP$. We also show $NE\not\subseteq NPT(P{tt}(NP)\cap Tally)$.