  We present developments and applications for the diagonalization of
shell-model hamiltonians in a discrete non-orthogonal basis (DNO-SM). The
method, and its actual numerical implementation CARINA, based on mean-field and
beyond-mean field techniques has already been applied in previous studies and
is focused on basis states selection optimization. The method is benchmarked
against a full set of $sd$ shell exact diagonalizations, and is applied for the
first time to the heavy deformed $^{254}$No nucleus.
