In [IPL2005],
Frandsen and Miltersen improved bounds on the circuit size $L(n)$ of the hardest Boolean function on $n$ input bits:
for some constant $c>0$:
\[
\left(1+\frac{\log n}{n}-\frac{c}{n}\right)
\frac{2^n}{n}
\leq
L(n)
\leq
\left(1+3\frac{\log n}{n}+\frac{c}{n}\right)
\frac{2^n}{n}.
\]
In this note,
we announce a modest improvement on the lower bound:
for some constant $c>0$ (and for any sufficiently large $n$),
\[
L(n) \geq
\left(1+2\frac{\log n}{n}-\frac{c}{n}\right)
\frac{2^n}{n}.
\]