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A backtrack-free Prolog construction method is available at

based on [anderson1997short]

A complete description with references can be found in:

Eric W. Weisstein. “Steiner Triple System.” From [MathWorld][2]—A Wolfram Web Resource.

[lindner2011topics]
Charles C Lindner and Alexander Rosa
Topics on steiner systems
2011

[kaski2008steiner]
Petteri Kaski, Patric R. J. Östergård, Svetlana Topalova, and Rosen Zlatarski
Steiner triple systems of order 19 and 21 with subsystems of order 7
Discrete Mathematics 308(13), 2008

[kaski2004steiner]
Petteri Kaski and Patric R. J. Östergård
The Steiner triple systems of order 19
Mathematics of Computation 73(248), 2004

[lagoon2004set]
Vitaly Lagoon and Peter J Stuckey
Set domain propagation using ROBDDs
Principles and Practice of Constraint Programming–CP 2004, 2004

[azevedo2003constraint]
Francisco Azevedo
Constraint Solving Over Multi-valued Logics: Application to Digital Circuits
2003

[anderson1997short]
Ian Anderson and Iiro Honkala
A short course in combinatorial designs
Internet Edition Spring 1997, 1997

[gervet1997interval]
Carmen Gervet
Interval propagation to reason about sets: Definition and implementation of a practical language
Constraints 1(3), 1997

[beldiceanu1990example]
Nicolas Beldiceanu
An example of introduction of global constraints in CHIP: Application to block theory problems
Technical Report Technical Report TR-LP-49, ECRC, Munich, Germany, 1990

[luneburg1989tools]
Heinz Lüneburg
Tools and fundamental constructions of combinatorial mathematics
1989

[babai1980almost]
László Babai
Almost all Steiner triple systems are asymmetric
Annals of Discrete Mathematics, 1980

[lindner1978steiner]
Charles C Lindner and Alexander Rosa
Steiner quadruple systems-a survey
Discrete Mathematics 22(2), 1978

[doyen1973embeddings]
Jean Doyen and Richard M Wilson
Embeddings of Steiner triple systems
Discrete Mathematics 5(3), 1973

[ray1971solution]
Dwijendra K Ray-Chaudhuri and Richard M Wilson
Solution of Kirkman’s schoolgirl problem
Proc. Symp. Pure Math, 1971

[hall1960automorphisms]
Marshall Hall
Automorphisms of Steiner triple systems
IBM Journal of Research and Development 4(5), 1960