  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 by utilizing dynamic programming and the
Lindstr\"om-Gessel-Viennot lemma. Our new bound is $b_n \geq 0.2721$ for
sufficiently large $n$. The result is based on a delicate interplay of
theoretical ideas and computer assistance.
