  Long Paths and Cycles in eulerian digraphs have gotten a lot of attention
recently. In this short note, we show how to use methods from Knierim, Larcher,
Martinsson, Noever (2021) to find paths of length $d/(\log d+1)$ in Eulerian
digraphs with average degree $d$, improving the recent result of
$\Omega(d^{1/2+1/40})$. Our result is optimal up to at most a logarithmic
factor.
