This question is about Joel Spencer's famous "six standard deviations" theorem. If you don't know the theorem, it's Theorem 1 in: 

Spencer, Joel. Six standard deviations suffice. Trans. Amer. Math. Soc. 289 (1985), no. 2, 679–706. [Full text PDF (open access)](http://www.ams.org/journals/tran/1985-289-02/S0002-9947-1985-0784009-0/S0002-9947-1985-0784009-0.pdf)


As noted at the end of the paper, the constant K which Spencer obtained is actually K=5.32.

Question: does anybody know of a proof of the Theorem which gives a smaller value for the constant?