  It is known that there is a close analogy between "Euclidean t-designs vs.
spherical t-designs" and "Relative t-designs in binary Hamming association
schemes vs. combinatorial t-designs". In this paper, we want to prove how much
we can develop a similar theory in the latter situation, imitating the theory
in the former one. We first prove that the weight function is constant on each
shell for tight relative t-designs on p shells on a wide class of Q-polynomial
association schemes, including Hamming association schemes. In the theory of
Euclidean t-designs on 2 concentric spheres (shells), it is known that the
structure of coherent configurations is naturally attached. However, it seems
difficult to prove this claim in a general context. In the case of tight
2-designs in combinatorial 2-designs, there are great many tight 2-designs,
i.e., symmetric 2-designs, while there are very few tight 2e-designs for e no
less than 2. So, as a starting point, we concentrate our study to the existence
problem of tight relative 2-designs, in particular on 2 shells, in binary
Hamming association schemes H(n,2). We prove that every tight relative
2-designs on 2 shells in H(n,2) has the structure of coherent configuration. We
determined all the possible parameters of coherent configurations attached to
such tight relative 2-designs for n at most 30. Moreover for each of them we
determined whether there exists such a tight relative 2-design or not, either
by constructing them from symmetric 2-designs or Hadamard matrices, or
theoretically showing the non-existence. In particular, we show that for n
congruent to 6 (mod 8), there exist such tight relative 2-designs whose weight
functions are not constant. These are the first examples of those with
non-constant weight.
