  A set S of unit vectors in n-dimensional Euclidean space is called spherical
two-distance set, if there are two numbers a and b, and inner products of
distinct vectors of S are either a or b. The largest cardinality g(n) of
spherical two-distance sets is not exceed n(n+3)/2. This upper bound is known
to be tight for n=2,6,22. The set of mid-points of the edges of a regular
simplex gives the lower bound L(n)=n(n+1)/2 for g(n.
  In this paper using the so-called polynomial method it is proved that for
nonnegative a+b the largest cardinality of S is not greater than L(n). For the
case a+b<0 we propose upper bounds on |S| which are based on Delsarte's method.
Using this we show that g(n)=L(n) for 6<n<22, 23<n<40, and g(23)=276 or 277.
