According to the Handbook of Combinatorial Designs, the only known example of a (27, 6, 5) design was given by Hanani. Even though a census of the designs with these parameters appears to be unfeasible, in this paper we show how some algebraic methods and the aid of a computer allow us to say that their number is at least 459. We show, in particular, that two of them are doubly point-transitive with their full automorphism groups being AΓL(1, 27) and AGL(1, 27). These two special designs are both flag-transitive and additive.
(27, 6, 5) designs with a nice automorphism group / Buratti, M.; Martinovic, F.; Nakic, A.. - In: THE AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 2202-3518. - 92:(2025), pp. 80-95.
(27, 6, 5) designs with a nice automorphism group
Buratti M.Primo
Writing – Original Draft Preparation
;Nakic A.
Writing – Original Draft Preparation
2025
Abstract
According to the Handbook of Combinatorial Designs, the only known example of a (27, 6, 5) design was given by Hanani. Even though a census of the designs with these parameters appears to be unfeasible, in this paper we show how some algebraic methods and the aid of a computer allow us to say that their number is at least 459. We show, in particular, that two of them are doubly point-transitive with their full automorphism groups being AΓL(1, 27) and AGL(1, 27). These two special designs are both flag-transitive and additive.| File | Dimensione | Formato | |
|---|---|---|---|
|
buratti_designs_2025.pdf
accesso aperto
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Creative commons
Dimensione
201.37 kB
Formato
Adobe PDF
|
201.37 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
