  A finite set X in the Euclidean space is called an s-inner product set if the
set of the usual inner products of any two distinct points in X has size s.
First, we give a special upper bound for the cardinality of an s-inner product
set on concentric spheres. The upper bound coincides with the known lower bound
for the size of a Euclidean 2s-design. Secondly, we prove the non-existence of
2- or 3-inner product sets on two concentric spheres attaining the upper bound
for any d>1. The efficient property needed to prove the upper bound for an
s-inner product set gives the new concept, inside s-inner product sets. We
characterize the most known tight Euclidean designs as inside s-inner product
sets attaining the upper bound.
