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

Grannell, M.; Griggs, T.; Mathon, R.

doi:10.1090/S0025-5718-98-00924-7

Steiner systems $S(5,6,v)$ with $v=72$ and $84$
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by M. J. Grannell, T. S. Griggs and R. A. Mathon PDF

Math. Comp. 67 (1998), 357-359 Request permission

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.

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