  Production of the (anti)hypertriton nuclei $\rm ^3_{\Lambda}H$ and $\rm
^3_{\overline \Lambda}\overline H$ in Cu+Cu interactions at
$\sqrt{s_{\rm{NN}}}=200$GeV is studied at three centrality bins of 0-10\%,
10-30\% and 30-60\% using the dynamically constrained phase-space coalescence
model together with [PACIAE] model simulations. The $\rm ^3H(^3\overline H)$
and $\rm ^3He(^3\overline {He})$ nuclei has been compared. It is indicated by
the study that the yields of light nuclei and hypernuclei increase rapidly from
peripheral to central collisions while their anti-particle to particle ratios
keep unchanged for different centrality bins. The strangeness population factor
$S_3=\rm{{^3_{\Lambda}H}/({^3{He}}\times \Lambda/p)}$ was found to be close to
unity, and was compatible with the STAR data and theoretical model calculation,
suggesting that the phase-space population of strange quarks is similar with
the ones of light quarks and the creation of deconfined high temperature quark
matter in Cu+Cu collisions.
