  Double-beta decay matrix elements (ME) for $^{76}Ge$ are calculated with
different quasi random phase approximation (QRPA)-based methods. First, the ME
for the two-neutrino mode are computed using two choices for the single
particle (s.p.) basis: i) $2-4\hbar\omega$ full shells and ii) $3-4\hbar\omega$
full shells. When calculated with the renormalized QRPA (RQRPA) and full-RQRPA
their values are rather dependent on the size of the single particle basis
used, while calculated with proton-neutron QRPA (pnQRPA) and second-QRPA
approaches such a dependence was found to be small. The Ikeda sum rule was well
fulfilled within pnQRPA for both choices of the s.p. basis and with a good
approximation within second-QRPA, while the RQRPA and full-RQRPA methods give
deviations up to 21%. Further, the ME for the neutrinoless mode are calculated
with the pnQRPA, RQRPA and full-RQRPA methods. They all give close results for
the calculation with the smaller basis (i), while for the larger basis (ii),
the results differ significantly either from one method to another or within
the same method. Finally, using the most recent experimental limit for the
$0\nu\beta\beta$ decay half-life of $^{76}Ge$ a critical discussion on the
upper limits for the neutrino mass parameter obtained with different
theoretical approaches is given.
