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We present measurements of the inclusive production of antideuterons in$e^+e^-$ annihilation into hadrons at $\approx 10.58 \mathrm{\,Ge\kern -0.1emV}$ center-of-mass energy and in $\Upsilon(1S,2S,3S)$ decays. The results areobtained using data collected by the BABAR detector at the PEP-IIelectron-positron collider. Assuming a fireball spectral shape for the emittedantideuteron momentum, we find $\mathcal{B}(\Upsilon(1S) \to \bar{d}X) = (2.81\pm 0.49 \mathrm{(stat)} {}^{+0.20}_{-0.24} \mathrm{(syst)})/! \times /!10^{-5}$, $\mathcal{B}(\Upsilon(2S) \to \bar{d}X) = (2.64 \pm 0.11\mathrm{(stat)} {}^{+0.26}_{-0.21} \mathrm{(syst)})/! \times /! 10^{-5}$,$\mathcal{B}(\Upsilon(3S) \to \bar{d}X) = (2.33 \pm 0.15 \mathrm{(stat)}{}^{+0.31}_{-0.28} \mathrm{(syst)})/! \times /! 10^{-5}$, and $\sigma (e^+e^-\to \bar{d}X) = (9.63 \pm 0.41 \mathrm{(stat)} {}^{+1.17}_{-1.01}\mathrm{(syst)}) \mbox{\,fb}$.

Antideuteron production in $\Upsilon(nS)$ decays and in $e^+e^- \to q\overline{q}$ at $\sqrt{s} \approx 10.58 \mathrm{\,Ge\kern -0.1em V}$