We present a new determination of the B and B_s meson decay constants using NRQCD b-quarks, HISQ light and strange valence quarks and the MILC collaboration N_f=2+1 lattices. The new calculations improve on HPQCDs earlier work with NRQCD b-quarks by replacing AsqTad with HISQ valence quarks, by including a more chiral MILC fine ensemble in the analysis, and by employing better tuned quark masses and overall scale. We find f_B = 0.191(9)GeV, f_{B_s} = 0.228(10)GeV and f_{B_s}/f_B = 1.188(18). Combining the new value for f_{B_s}/f_B with a recent very precise determination of the B_s meson decay constant based on HISQ b-quarks, f_{B_s} = 0.225(4)GeV, leads to f_B = 0.189(4)GeV. With errors of just 2.1% this represents the most precise f_B available today.
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