Pooling designs with high degree of error correction in singular linear space over finite fields

In this paper, we construct a family of new pooling designs based on the singular linear spaces and related counting theorems. By analyzing its disjunct properties, it turns out that the new design is superior to the existing designs under the same experimental efficiency. Additionally, we compare our pooling design with Liu et al.'s with regard to the parameters of construction. At last, the relevant proof of our pooling designs is given.