  Lattice quantum chromodynamics is used to constrain the interactions of two
octet baryons at the SU(3) flavor-symmetric point, with quark masses that are
heavier than those in nature (equal to that of the physical strange quark mass
and corresponding to a pion mass of $\approx 806~\tt{MeV}$). Specifically, the
S-wave scattering phase shifts of two-baryon systems at low energies are
obtained with the application of L\"uscher's formalism, mapping the energy
eigenvalues of two interacting baryons in a finite volume to the two-particle
scattering amplitudes below the relevant inelastic thresholds. The values of
the leading-order low-energy scattering parameters in the irreducible
representations of SU(3) are consistent with an approximate SU(6) spin-flavor
symmetry in the nuclear and hypernuclear forces that is predicted in the
large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between
two baryons are constrained at this value of the quark masses, and their values
indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible
representations containing the $NN~({^1}S_0)$, $NN~({^3}S_1)$ and
$\frac{1}{\sqrt{2}}(\Xi^0n+\Xi^-p)~({^3}S_1)$ channels unambiguously exhibit a
single bound state, while the irreducible representation containing the
$\Sigma^+ p~({^3}S_1)$ channel exhibits a state that is consistent with either
a bound state or a scattering state close to threshold. These results are in
agreement with the previous conclusions of the NPLQCD collaboration regarding
the existence of two-nucleon bound states at this value of the quark masses.
