We prove that the Grothendieck constant $K_G < \fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$. This improves on the work of Braverman, Makarychev, Makarychev, and Naor (2011), who proved that $K_G < \fracπ{2 \log (1+ \sqrt{2})} - ε$ for an unspecified $ε>0$.

翻译：我们证明格罗滕迪克常数 $K_G < \fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$。这改进了 Braverman、Makarychev、Makarychev 和 Naor（2011）的工作，他们证明了 $K_G < \fracπ{2 \log (1+ \sqrt{2})} - ε$，其中 $ε>0$ 未具体给出。