Geodesic
A family of 4-designs on 26 points
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 843-860

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Using the Kramer-Mesner method, $4$-$(26,6,\lambda)$ designs with $PSL(2,25)$ as a group of automorphisms and with $\lambda$ in the set $\{30,51,60,81,90,111\}$ are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called ``quasi-designs''. Actions of groups $PSL(2,25)$, $PGL(2,25)$ and twisted $PGL(2,25)$ are being compared. It is shown that there exist $4$-$(26,6,\lambda)$ designs with $PGL(2,25)$, respectively twisted $PGL(2,25)$ as a group of automorphisms and with $\lambda$ in the set $\{51,60,81,90,111\}$. With $\lambda$ in the set $\{60,81\}$, there exist designs which possess all three considered groups as groups of automorphisms. An overview of $t$-$(q+1,k,\lambda)$ designs with $PSL(2,q)$ as group of automorphisms and with $(t,k) \in \{(4,5), (4,6), (5,6)\}$ is included.
Classification : 05B05, 05B30
Keywords: block designs; orbits; projective linear group; projective special linear group; twisted projective linear group; Kramer-Mesner method 
@article{CMUC_1996__37_4_a16,
     author = {Acketa, Dragan M. and Mudrinski, Vojislav},
     title = {A family of 4-designs on 26 points},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {843--860},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {1996},
     mrnumber = {1440715},
     zbl = {0886.05038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996__37_4_a16/}
}
TY  - JOUR
AU  - Acketa, Dragan M.
AU  - Mudrinski, Vojislav
TI  - A family of 4-designs on 26 points
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1996
SP  - 843
EP  - 860
VL  - 37
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1996__37_4_a16/
LA  - en
ID  - CMUC_1996__37_4_a16
ER  - 
%0 Journal Article
%A Acketa, Dragan M.
%A Mudrinski, Vojislav
%T A family of 4-designs on 26 points
%J Commentationes Mathematicae Universitatis Carolinae
%D 1996
%P 843-860
%V 37
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1996__37_4_a16/
%G en
%F CMUC_1996__37_4_a16
Acketa, Dragan M.; Mudrinski, Vojislav. A family of 4-designs on 26 points. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 843-860. http://geodesic.mathdoc.fr/item/CMUC_1996__37_4_a16/