A construction of dzdz-disjunct matrices in a dual space of symplectic space

In this paper, we construct a dzdz-disjunct   matrix with subspaces in a dual space of symplectic space Fq(2ν), then give its several properties and a new definition, ratio efficiency t/nt/n. As the smaller the ratio efficiency is, the better the pooling design is. We discuss the ratio efficiency of this construction and compare it with others, such as in [Anthony J. Macula, A simple construction of dd-disjunct matrices with certain constant weights, Discrete Mathematics 162 (1996) 311–312; A.G. D’yachkov, Frank K. Hwang, Antony J. Macula, Pavel A. Vilenkin, Chih-wenWeng, A construction of pooling designs with some happy surprises, Journal of Computational Biology 12 (2005) 1129–1136].