ISSN:
1573-7586
Keywords:
t-design
;
Kramer-Mesner method
;
intersection number
;
isomorphism problem
;
group action
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We show the existence of simple 8-(31,10,93) and 8-(31,10,100) designs. For each value of λ we show 3 designs in full detail. The designs are constructed with a prescribed group of automorphisms PSL(3,5) using the method of Kramer and Mesner KramerMesner76. They are the first 8-designs with small parameters which are known explicitly. We do not yet know if PSL(3,5) is the full group of automorphisms of the given designs. There are altogether 138 designs with λ = 93 and 1658 designs with λ = 100 and PSL(3,5) as a group of automorphisms. We prove that they are all pairwise non-isomorphic. For this purpose, a brief account on the intersection numbers of these designs is given. The proof is done in two different ways. At first, a quite general group theoretic observation shows that there are no isomorphisms. In a second approach we use the block intersection types as invariants, they classify the designs completely.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008263724078
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