  This work presents new constraints on the existence and the binding energy of
a possible $\Lambda$-$\Lambda$ bound state, the H-dibaryon, derived from
$\Lambda$-$\Lambda$ femtoscopic measurements by the ALICE collaboration. The
results are obtained from a new measurement using the femtoscopy technique in
pp collisions at $\sqrt{s}=13$ TeV and p-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, combined with previously published results
from p-Pb collisions at $\sqrt{s}=7$ TeV. The $\Lambda$-$\Lambda$ scattering
parameter space, spanned by the inverse scattering length $f_0^{-1}$ and the
effective range $d_0$, is constrained by comparing the measured
$\Lambda$-$\Lambda$ correlation function with calculations obtained within the
Lednicky model. The data are compatible with hypernuclei results and lattice
computations, both predicting a shallow attractive interaction, and permit to
test different theoretical approaches describing the $\Lambda$-$\Lambda$
interaction. The region in the $(f_0^{-1},d_0)$ plane which would accommodate a
$\Lambda$-$\Lambda$ bound state is substantially restricted compared to
previous studies. The binding energy of the possible $\Lambda$-$\Lambda$ bound
state is estimated within an effective-range expansion approach and is found to
be
$B_{\Lambda\Lambda}=3.2^{+1.6}_{-2.4}\mathrm{(stat)}^{+1.8}_{-1.0}\mathrm{(syst)}$
MeV.
