Characteristics Are Not Designed For A Class Grouping In The 2 Orthogonal Space

In recent years, non-adaptive group testing's study is very actively, because ithas many practical applications. Designing good error-tolerant pooling design isa central problem in the area of non-adaptive group testing. A d-disjunct matrixcorresponds precisely to a pooling design which can identify at most d negativeitems using t tests from n items. Due to various reasons, it is inevitable to produceerroneous outcomes in the test. Designing the error-tolerant pooling design(disjunctmatrix) is very necessary. Macula firstly proposed the notion of d^z-disjunct matrixto reflect the error-correction capability of a d-disjunct matrix.In this paper, we use subspace of type (m, 2s, s) in the orthogonal space F_q^2vto construct a d^z-disjunct matrix M(2v, m, m₁) and prove that z is optimal whend≤q + 1, that is, the bound is tight for d≤q + 1.For the above d^z- disjunct matrix M(2v, m, m₁), we investigate tight boundsfor the case when q + 1 < d≤N(m-1,2s, s; m, 2s, s; 2v,△) using the arrange-ment problem subspace of type (m-1,2s, s) in the subspace of type (m, 2s, s).