  We explore the implications of t-b-tau (and b-tau) Yukawa coupling
unification condition on the fundamental parameter space and sparticle
spectroscopy in the minimal gauge mediated supersymmetry breaking (mGMSB)
model. We find that this scenario prefers values of the CP-odd Higgs mass m_A >
1 TeV, with all colored sparticle masses above 3 TeV. These predictions will be
hard to test at LHC13 but they may be testable at HE-LHC 33 TeV or a 100 TeV
collider. Both t-b-tau and b-tau Yukawa coupling unifications prefer a
relatively light gravitino with mass < 30 eV, which makes it a candidate hot
dark matter particle. However, it cannot account for more than 15 % of the
observed dark matter density.
