A Steiner quadruple system on $2^n$ points is called semi-Boolean if all of its derived triple systems on $2^n-1$ points are isomorphic to the classical one having as blocks the lines in PG$(n-1,2)$. A construction of semi-Boolean Steiner quadruple systems is given, and this construction is used to prove that there are at least $2^{3(n-4)/2}$ non-isomorphic semi-Boolean systems that are also resolvable and that admit a regular group of automorphisms.
A lower bound on the number of Semi-Boolean quadruple systems
BURATTI, Marco;
2003
Abstract
A Steiner quadruple system on $2^n$ points is called semi-Boolean if all of its derived triple systems on $2^n-1$ points are isomorphic to the classical one having as blocks the lines in PG$(n-1,2)$. A construction of semi-Boolean Steiner quadruple systems is given, and this construction is used to prove that there are at least $2^{3(n-4)/2}$ non-isomorphic semi-Boolean systems that are also resolvable and that admit a regular group of automorphisms.File in questo prodotto:
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