We construct an explicit distribution $\mathbf{D}$ over $\{0,1\}^N$ that exhibits an essentially optimal separation between adaptive and non-adaptive cell-probe sampling. The distribution can be sampled exactly when each output bit is allowed two adaptive probes to an arbitrarily long sequence of independent uniform symbols from $[N]$. In contrast, any non-adaptive sampler requires $\widetildeΩ(N)$ non-adaptive cell probes to generate a distribution with total variation distance less than $1-o(1)$ from $\mathbf{D}$. This provides a $2$-vs-$\widetildeΩ(N)$ separation for sampling with adaptive versus non-adaptive cell probes, improving upon the $2$-vs-$\widetildeΩ(\log N)$ separation of Yu and Zhan (ITCS '24) and the $(\log N)^{O(1)}$-vs-$N^{Ω(1)}$ separation of Alekseev, Göös, Myasnikov, Riazanov, and Sokolov (STOC '26).

翻译：我们构造了一个显式分布 $\mathbf{D}$ over $\{0,1\}^N$，该分布在自适应与非自适应单元探针采样之间展现出本质最优的分离。当每个输出比特允许对 $[N]$ 中任意长的独立均匀符号序列进行两次自适应探针时，该分布可被精确采样。相比之下，任何非自适应采样器需要 $\widetildeΩ(N)$ 次非自适应单元探针，才能生成与 $\mathbf{D}$ 总变差距离小于 $1-o(1)$ 的分布。这给出了自适应与非自适应单元探针采样之间 $2$-vs-$\widetildeΩ(N)$ 的分离，改进了 Yu 和 Zhan (ITCS '24) 的 $2$-vs-$\widetildeΩ(\log N)$ 分离，以及 Alekseev、Göös、Myasnikov、Riazanov 和 Sokolov (STOC '26) 的 $(\log N)^{O(1)}$-vs-$N^{Ω(1)}$ 分离。