In a recent breakthrough, Chen, Hirahara and Ren prove that $\mathsf{S_2E}/_1 \not\subset \mathsf{SIZE}[2^n/n]$ by giving a single-valued $\mathsf{FS_2P}$ algorithm for the Range Avoidance Problem ($\mathsf{Avoid}$) that works for infinitely many input size $n$. Building on their work, we present a simple single-valued $\mathsf{FS_2P}$ algorithm for $\mathsf{Avoid}$ that works for all input size $n$. As a result, we obtain the circuit lower bound $\mathsf{S_2E} \not\subset \mathsf{SIZE}[2^n/n]$ and many other corollaries: 1. Near-maximum circuit lower bound for $\mathsf{\Sigma_2E} \cap \mathsf{\Pi_2E}$ and $\mathsf{ZPE}^{\mathsf{NP}}$. 2. Pseudodeterministic $\mathsf{FZPP}^{\mathsf{NP}}$ constructions for: Ramsey graphs, rigid matrices, pseudorandom generators, two-source extractors, linear codes, hard truth tables, and $K^{poly}$-random strings.

翻译：在最近的一项突破性工作中，Chen、Hirahara和Ren通过为范围回避问题（$\mathsf{Avoid}$）设计一个在无穷多个输入规模$n$上有效的单值$\mathsf{FS_2P}$算法，证明了$\mathsf{S_2E}/_1 \not\subset \mathsf{SIZE}[2^n/n]$。基于他们的工作，我们提出了一个简单的单值$\mathsf{FS_2P}$算法用于$\mathsf{Avoid}$，该算法对所有输入规模$n$均有效。由此，我们得到电路下界$\mathsf{S_2E} \not\subset \mathsf{SIZE}[2^n/n]$及许多其他推论：1. $\mathsf{\Sigma_2E} \cap \mathsf{\Pi_2E}$和$\mathsf{ZPE}^{\mathsf{NP}}$的接近最大电路下界。2. 伪确定性$\mathsf{FZPP}^{\mathsf{NP}}$构造：拉姆齐图、刚性矩阵、伪随机生成器、双源提取器、线性码、硬真值表和$K^{poly}$随机字符串。