The Grothendieck Constant is Strictly Smaller than Krivine's Bound. Braverman, M., Makarychev, K., Makarychev, Y., & Naor, A. In FOCS, pages 453-462, 2011.
The Grothendieck Constant is Strictly Smaller than Krivine's Bound [link]Link  bibtex   
@inproceedings{DBLP:conf/focs/BravermanMMN11,
  author    = {Mark Braverman and
               Konstantin Makarychev and
               Yury Makarychev and
               Assaf Naor},
  title     = {The Grothendieck Constant is Strictly Smaller than Krivine's
               Bound},
  booktitle = {FOCS},
  year      = {2011},
  pages     = {453-462},
  ee        = {http://dx.doi.org/10.1109/FOCS.2011.77},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

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