| Title:
|
A family of 4-designs on 26 points (English) |
| Author:
|
Acketa, Dragan M. |
| Author:
|
Mudrinski, Vojislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
843-860 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
block designs |
| Keyword:
|
orbits |
| Keyword:
|
projective linear group |
| Keyword:
|
projective special linear group |
| Keyword:
|
twisted projective linear group |
| Keyword:
|
Kramer-Mesner method |
| MSC:
|
05B05 |
| MSC:
|
05B30 |
| idZBL:
|
Zbl 0886.05038 |
| idMR:
|
MR1440715 |
| . |
| Date available:
|
2009-01-08T18:28:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118892 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[7] Dautović S., Acketa D.M., Mudrinski V.: A graph approach to isomorphism testing of $4$-$(48,5,\lambda)$ designs arising from $PSL(2,47)$.submitted. |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[13] Janko Z., Tonchev V.: Private communication.. |
| Reference:
|
[14] Kramer E.S., Leavitt D.W., Magliveras S.S.: Construction procedures for $t$-designs and the existence of new simple $6$-designs.Ann. Discrete Math. 26 (1985), 247-274. Zbl 0585.05002, MR 0833794 |
| Reference:
|
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| Reference:
|
[16] Kreher D.L., Radziszowski S.P.: The existence of simple $6$-$(14,7,4)$ designs.Jour. of Combinatorial Theory, Ser. A 43 (1986), 237-243. Zbl 0647.05013, MR 0867649 |
| Reference:
|
[17] Kreher D.L., Radziszowski S.P.: Simple $5$-$(28,6,\lambda)$ designs from $PSL_2(27)$.Ann. Discrete Math. 34 (1987), 315-318. MR 0920656 |
| . |
