  We present a search for the possible $I(J^{P})=0(2^{+})$ tetraquark state
with $ss{\bar s}{\bar s}$ quark content in quenched improved anisotropic
lattice QCD. Using various local and non-local interpolating fields we
determine the energies of ground-state and second ground state using
variational method. The state is found to be consistent with two-particle
scattering state, which is checked to exhibit the expected volume dependence of
the spectral weights. In the physical limit, we obtain for the ground state, a
mass of $2123(33)(58)$ MeV which is higher than the mass of experimentally
observed $f(2010)$. The lattice resonance signal obtained in the physical
region does not support a localized $J^{P} =2^{+}$ tetraquark state in the pion
mass region of $300 - 800$ MeV. We conclude that the $4q$ system in question
appears as a two-particle scattering state in the quark mass region explored
here.
