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Abstract A pooling space is defined to be a ranked partially ordered set with atomic intervalsWe show how to construct non-adaptive pooling designs from a pooling spaceOur pooling designs are e−error de-tecting for some e; moreover e can be chosen to be very large compared with the maximal number of defective itemsEight new classes of non-adaptive pooling designs are given
which are related to the Hamming matroid
the attenuated space
and six classical polar spaces

Keywords: pooling space
pooling design
ranked partially ordered set
atomic interval

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[1 ] A. J. Macula, A simple construction of

d−disjunct matrices with certain constant

weights, Discrete Math., 162:311-312, 1996. [2 ] A. J. Macula, Probabilistic nonadaptive group

testing in the presence of errors and dna li-brary screening, Annals of Combinatorics, 3:61-69, 1999.

[3 ] H. Ngo and D. Zu, A Survey on Combina-torial Group Testing Algorithms with Applica-tions to DNA Library Screening, DIMACS Se-ries in Discrete Mathematics and Theoretical Computer Science, 55:171-182, 2000.

[4 ] H. Ngo and D. Du, New Constructions of Non-Adaptive and Error-Tolerance Pooling Designs, Discrete Math., 243:161-170, 2002.

[5 ] P. Terwilliger, Quantum matroids, Progress in algebraic combinatorics (Fukuoka, 1993), 323– 441, Adv. Stud. Pure Math., 24, Math. Soc. Japan, Tokyo, 1996.

[6 ] C. Weng, D-bounded Distance-regular Graphs, Europ. J. Combinatorics, 18:211-229, 1997.

[7 ] T. Huang and C. Weng, Pooling Spaces and Non-Adaptive Pooling Designs, preprint.