Pooling designs with surprisingly high degree of error correction in a finite vector space

Pooling designs are standard experimental tools in many biotechnical applications. It is well-known that all famous pooling designs are constructed from mathematical structures by the “containment matrix” method. In particular, Macula’s designs (resp. Ngo and Du’s designs) are constructed by means of the containment relation of subsets (resp. subspaces) in a finite set (resp. vector space). In [J. Guo, K. Wang, A construction of pooling designs with high degree of error correction, J. Combin. Theory Ser. A 118 (2011) 2056–2058], we generalized Macula’s designs and obtained a family of pooling designs with higher degree of error correction. In this paper we consider, as a generalization of Ngo and Du’s designs, qq-analogue of the above designs, and obtain a family of pooling designs with surprisingly high degree of error correction. Our designs and Ngo and Du’s designs have the same numbers of items and pools, but the error-tolerance property of our design is much better than that of Ngo and Du’s designs when the dimension of the space is large enough.