Effect of L-Mode Electric Field Bifurcations and Edge Stochasticity on the L-H Transition Power Threshold with Applied n$=$3 Resonant Magnetic Perturbations**

H-mode access in ITER-similar-shape plasmas in DIII-D ($n_{\mathrm{e}}=$1.5-5x10$^{\mathrm{19}}$m$^{\mathrm{-3}}$, $B_{\mathrm{t}}=$1.9-2T, $I_{\mathrm{p}}=$1.5MA, $q_{\mathrm{95}}=$3.6) with applied n$=$3 Resonant Magnetic Perturbations (RMP) is found to depend on edge collisionality like $P_{\mbox{LH}} /P_{\mbox{LH-08}} \sim (\nu \ast )^{-0.5}$. This is a concern for ECH-heated, low collisionality plasmas on ITER since RMP may be applied before the L-H transition to safely suppress the first ELM. Bifurcations to positive radial electric field, increased toroidal co-rotation, and reduced edge $E\times B$ shear are observed when RMP fields are screened, preventing H-mode access at high applied RMP within the heating power range explored (P$_{\mathrm{loss}}\le $4 MW). Evidence of restored H-mode access with n$=$3 RMP field penetration is presented. An edge stochasticity model accounting for electron loss in the stochastic boundary layer can explain the experimental findings. The observed increase in $P_{\mathrm{LH}}$ at low collisionality is attributed to a reduced ExB shearing rate $\omega _{\mbox{E}\times \mbox{B}} $ and an increased normalized growth rate $\gamma _{\mbox{L}} /\omega_{\mbox{E}\times \mbox{B}} $.