  We provide a construction of binary pseudorandom sequences based on Hardy
fields $\mathcal{H}$ as considered by Boshernitzan. In particular we give upper
bounds for the well distribution measure and the correlation measure defined by
Mauduit and S\'ark\"ozy. Finally we show that the correlation measure of order
$s$ is small only if $s$ is small compared to the ``growth exponent'' of
$\mathcal{H}$.
