Recent lattice results have shown that there is no Standard Model ( SM ) electroweak phase transition ( EWPT ) for Higgs boson masses above \approx 72 GeV , which is below the present experimental limit .
According to perturbation theory and 3-dimensional ( 3d ) lattice simulations there could be an EWPT in the Minimal Supersymmetric Standard Model ( MSSM ) that is strong enough for baryogenesis up to m _ { h } \approx 105 GeV .
In this letter we present the results of our large scale 4-dimensional ( 4d ) lattice simulations for the MSSM EWPT .
We carried out infinite volume and continuum limits and found a transition whose strength agrees well with perturbation theory , allowing MSSM electroweak baryogenesis at least up to m _ { h } = 103 \pm 4 GeV .
We determined the properties of the bubble wall that are important for a successful baryogenesis .

PACS numbers : 11.10.Wx , 11.15.Ha , 12.60.Jv , 98.80.Cq