Abstract
The subject of this paper are some constructions of Steiner designs with blocks of two sizes that differ by one. The study of such designs is motivated by a combinatorial lower bound on the minimum number of individual tests at the second stage of a 2-stage disjunctive testing algorithm.
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References
Baker RD (1976) Partitioning the planes of AG 2m (2) into 2-designs. Discrete Math 15:205–211
Beth T, Jungnickel D, Lenz H (1999) Design theory, 2nd edn. Cambridge University Press, Cambridge
Colbourn CJ, Dinitz JF (eds) (1996) The CRC handbook of combinatorial designs. CRC, Boca Raton
Du D-Z, Hwang FK (1993) Combinatorial group testing and its applications. World Scientific, Singapore
Levenshtein VI (2003) A universal bound for a covering in regular posets and its application to pool testing. Discret Math 266:293–309
Semakov NV, Zinoviev VA, Zaitsev GV (1973) Interrelation of preparata and Hamming codes and extension of Hamming codes to new double-error-correcting codes. In: Proceedings of the 2nd international symposium on information theory, pp 257–263, Tsakhadsor, Armenia, 1971. Academiai Kiado, Budapest
Teirlinck L (1994) Some new 2-resolvable Steiner quadruple systems. Des Codes Cryptogr 4:5–10
Tonchev VD (2003) A formula for the number of Steiner quadruple systems on 2n points of 2-rank 2n−n. J Comb Des 11:260–274
Tonchev VD (1996) A class of Steiner 4-wise balanced designs derived from Preparata codes. J Comb Des 3:203–204
Wilson RM (1972a) An existence theory for pairwise balanced designs, part I. J Comb Theory Ser A 13:222–245
Wilson RM (1972b) An existence theory for pairwise balanced designs, part II. J Comb Theory Ser A 13:246–273
Wilson RM (1975) An existence theory for pairwise balanced designs, part III. J Comb Theory Ser A 18:71–79
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Tonchev, V.D. Steiner systems for two-stage disjunctive testing. J Comb Optim 15, 1–6 (2008). https://doi.org/10.1007/s10878-007-9079-z
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DOI: https://doi.org/10.1007/s10878-007-9079-z