1 research outputs found
Some Bounds for the Number of Blocks III
Let be a pair of point set and
a set consists of point subsets of which are called
blocks. Let be the maximal cardinality of the intersections between the
distinct two blocks in . The triple is called the
parameter of . Let be the number of the blocks in .
It is shown that inequality
holds for each satisfying , in the paper: Some Bounds for
the Number of Blocks, Europ. J. Combinatorics 22 (2001), 91--94, by R. Noda. If
achieves the upper bound, is called a design. In
the paper, an upper bound and a lower bound, , for of a design are
given. In the present paper we consider the cases when does not achieve the
upper bound or lower bound given above, and get new more strict bounds for
respectively. We apply this bound to the problem of the perfect -codes in
the Johnson scheme, and improve the bound given by Roos in 1983.Comment: Stylistic corrections are made. References are adde