  We construct optimal flat functions in Carleman-Roumieu ultraholomorphic
classes associated to general strongly nonquasianalytic weight sequences, and
defined on sectors of suitably restricted opening. A general procedure is
presented in order to obtain linear continuous extension operators, right
inverses of the Borel map, for the case of regular weight sequences in the
sense of Dyn'kin. Finally, we discuss some examples (including the well-known
$q$-Gevrey case) where such optimal flat functions can be obtained in a more
explicit way.
