  We show a simple explicit construction of an $2^{\Tilde{O}(\sqrt{\log n})}$
Ramsey graph. That is, we provide a $\poly(n)$-time algorithm to output the
adjacency matrix of an undirected $n$-vertex graph with no clique or
independent set of size $2^{\e \sqrt{\log n}\log\log n}$ for every $\e>0$.
  Our construction has the very serious disadvantage over the well-known
construction of Frankl and Wilson \cite{FranklWi81} that it is only explicit
and not very explicit, in the sense that we do \emph{not} provide a
poly-logarithmic time algorithm to compute the neighborhood relation. The main
advantage of this construction is its extreme simplicity. It is also somewhat
surprising that even though we use a completely different approach we get a
bound which essentially equals the bound of \cite{FranklWi81}. This
construction is quite simple and was obtained independently by others as
well\footnote{P.~Pudlak, personal communications, July 2004.} but as far as we
know has not been published elsewhere.
