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Forbes, Anthony; Grannell, Mike and Griggs, Terry
(2007).
Abstract
Quattrochi and Rinaldi introduced the idea of - isomorphism between Steiner systems. In this paper we study this concept in the context of Steiner triple systems. The main result is that for any positive integer
, there exists
such that for all admissible
and for each STS
(say
), there exists an STS
(say
) such that for some
,
is strictly
-isomorphic to
. We also prove that for all admissible
, there exist two STS
s which are strictly
-isomorphic. Define the distance between two Steiner triple systems
and
of the same order to be the minimum volume of a trade
which transforms
into a system isomorphic to
. We determine the distance between any two Steiner triple systems of order 15 and, further, give a complete classification of strictly
-isomorphic and
-isomorphic pairs of STS
s.