The hyperon-hyperon potentials due to a recent SU(3) Nijmegen soft-core potential model are incorporated within a relativistic mean field calculation of strange hadronic matter. We find considerably higher binding energy in bulk matter compared to several recent calculations which constrain the composition of matter. For small strangeness fractions (f(S)less than or similar to 1), matter is dominated by N Lambda Xi composition and the calculated binding energy closely follows that calculated by using the hyperon potentials of our previous calculations. For larger strangeness fractions (f(S)greater than or similar to 1), the calculated binding energy increases substantially beyond any previous calculation due to a phase transition into N Sigma Xi dominated matter. We also compare bulk matter calculations with finite system calculations, again highlighting the consequences of reducing the Coulomb destabilizing effects in finite strange systems.
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