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BIBD's for (13, 5, 5), (16, 6, 5) and (21, 6, 4) Possessing Possibly an Automorphism of Order 3 (CROSBI ID 172307)

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Martinjak, Ivica ; Pavčević, Mario-Osvin BIBD's for (13, 5, 5), (16, 6, 5) and (21, 6, 4) Possessing Possibly an Automorphism of Order 3 // International Journal of Social, Behavioral, Educational, Economic, Business and Industrial Engineering, 58 (2009), 902-905

Podaci o odgovornosti

Martinjak, Ivica ; Pavčević, Mario-Osvin

engleski

BIBD's for (13, 5, 5), (16, 6, 5) and (21, 6, 4) Possessing Possibly an Automorphism of Order 3

When trying to enumerate all BIBD's for given parameters, their natural solution space appears to be huge and grows extremely with the number of points of the design. Therefore, constructive enumerations are often carried out by assuming additional constraints on design's structure, automorphisms being mostly used ones. It remains a hard task to construct desgins with trivial automorphism group - those with no additional symmetry - although it is believed that most of the BIBD's belong to that case. In this paper, very many new designs with parameters 2-(13, 5, 5), 2-(16, 6, 5) and 2-(21, 6, 4) are constructed, assuming an action of an automorphism of order 3. Even more, it was possible to construct millions of such designs with no non-trivial automorphisms.

BIBD; incidence matrix; automorphism group; tactical decomposition; deterministic algorithm

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Podaci o izdanju

58

2009.

902-905

objavljeno

2010-376X

2010-3778

Povezanost rada

Računarstvo, Matematika

Indeksiranost