  In the present note, we prove new lower bounds on large values of character
sums $\Delta(x,q):=\max_{\chi \neq \chi_0} \vert \sum_{n\leq x} \chi(n)\vert$
in certain ranges of $x$. Employing an implementation of the resonance method
developed in a work involving the author in order to exhibit large values of
$L$- functions, we improve some results of Hough in the range $\log x =
o(\sqrt{\log q})$. Our results are expressed using the counting function of
$y$- friable integers less than $x$ where we improve the level of smoothness
$y$ for short intervals.
