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Further results on the existence of super-simple pairwise balanced designs with block sizes 3 and 4. (English) Zbl 1401.05048

Summary: In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple pairwise balanced designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this paper, the super-simple pairwise balanced designs with block sizes 3 and 4 are investigated and it is proved that the necessary conditions for the existence of a super-simple \((v, \{3,4\}, \lambda)\)-PBD for \(\lambda = 7,9\) and \(\lambda = 2k\), \(k\geq 1\), are sufficient with seven possible exceptions. In the end, several optical orthogonal codes and superimposed codes are given.

MSC:

05B05 Combinatorial aspects of block designs
51E05 General block designs in finite geometry
62K10 Statistical block designs
94C30 Applications of design theory to circuits and networks
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