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Steiner systems $S(5,6,v)$ with $v=72$ and $84$

Author(s): M. J. Grannell; T. S. Griggs; R. A. Mathon.
Journal: Math. Comp. 67 (1998), 357-359.
MSC (1991): Primary 05B05
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Abstract: It is proved that there are precisely 4204 pairwise non-isomorphic Steiner systems $S(5,6,72)$ invariant under the group $\mathrm{PSL}_2(71)$ and which can be constructed using only short orbits.

It is further proved that there are precisely 38717 pairwise non-isomorphic Steiner systems $S(5,6,84)$ invariant under the group $\mathrm{PSL}_2(83)$ and which can be constructed using only short orbits.

References:

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5.: W. H. Mills, A new 5-design, Ars Combinatoria 6 (1978), 193-195. MR 81f:05026
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7.: E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1938), 256-264.


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