Arrangements of pseudolines are classic objects in discrete and computational geometry. They have been studied with increasing intensity since their introduction almost 100 years ago. The study of the number $B_n$ of non-isomorphic simple arrangements of $n$ pseudolines goes back to Goodman and Pollack, Knuth, and others. It is known that $B_n$ is in the order of $2^{\Theta(n^2)}$ and finding asymptotic bounds on $b_n = \frac{\log_2(B_n)}{n^2}$ remains a challenging task. In 2011, Felsner and Valtr showed that $0.1887 \leq b_n \le 0.6571$ for sufficiently large $n$. The upper bound remains untouched but in 2020 Dumitrescu and Mandal improved the lower bound constant to $0.2083$. Their approach utilizes the known values of $B_n$ for up to $n=12$. We tackle the lower bound with a dynamic programming scheme. Our new bound is $b_n \geq 0.2526$ for sufficiently large $n$. The result is based on a delicate interplay of theoretical ideas and computer assistance.

翻译：伪线排列是离散与计算几何中的经典对象。自约一百年前被引入以来，对其的研究力度持续增强。对由$n$条伪线构成的非同构简单排列数量$B_n$的研究可追溯至Goodman、Pollack、Knuth等人。已知$B_n$的数量级为$2^{\Theta(n^2)}$，而寻找$b_n = \frac{\log_2(B_n)}{n^2}$的渐近界仍是一项具有挑战性的任务。2011年，Felsner与Valtr证明对于足够大的$n$，有$0.1887 \leq b_n \le 0.6571$。上界至今未被改进，但2020年Dumitrescu与Mandal将下界常数提升至$0.2083$，其方法利用了$n \leq 12$时$B_n$的已知值。我们采用动态规划方案攻克下界问题。对于足够大的$n$，新界为$b_n \geq 0.2526$。该结果基于理论见解与计算机辅助的精密协同。