  The observed mass pattern of scalar resonances below 1 GeV gives preference
to the tetraquark assignment over the conventional $\bar qq$ assignment for
these states. We present a search for tetraquarks with isospins 0, 1/2, 1 in
lattice QCD, where the isospin channels 1/2 and 1 have not been studied before.
We determine three energy levels in each isospin channel using the variational
method. The scattering states and possible tetraquark states are distinguished
by considering the volume-dependence of spectral weights and by considering the
time-dependence of correlators near t~T/2. We find no indication for light
tetraquarks at our range of pion masses 344-576 MeV.
