The Fisher Type Lower Bound And An Orthogonal Base For The Relative 2-Designs In H(n, 3)

The theory of relative t-design on Q-polynomial association scheme is one of themain objects of the theory of design. Professor Bannai, the algebraic combinatoricsexpert, pointed out that it is extremely important to obtain the Fisher type lower boundfor the relative t-design s, since only based on this can we discuss tight relative t-design s.We use the theory of association scheme and the properties of the vector space and linearalgebra to obtain Fisher type lower bound in a very explicit form for relative 2-designsin Hamming association scheme H(n, 3), and construct an orthogonal base.This thesis is divided into three chapters.In Chapter 1, we introduce the definitions of association schemes, relative t-design sand Fisher type lower bound, and recall some related facts.In Chapter 2, we obtain Fisher type lower bound in a very explicit form for relative2-designs in Hamming association scheme H(n, 3).In Chapter 3, when(Y, w) is a tight relative 2-design supported by two shells, weconstruct an orthogonal base of L0(S) + L1(S). Furthermore, we obtain the calculationformulas of the components of this orthogonal base at different points.