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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.

Charles C Lindner and Alexander Rosa
Topics on steiner systems

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), 2732–2741, 2008

Petteri Kaski and Patric R. J. Östergård
The Steiner triple systems of order 19
Mathematics of Computation 73(248), 2075–2092, 2004

Vitaly Lagoon and Peter J Stuckey
Set domain propagation using ROBDDs
Principles and Practice of Constraint Programming–CP 2004, 347–361, 2004

Francisco Azevedo
Constraint Solving Over Multi-valued Logics: Application to Digital Circuits
IOS Press

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

Carmen Gervet
Interval propagation to reason about sets: Definition and implementation of a practical language
Constraints 1(3), 191–244, 1997

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

Heinz Lüneburg
Tools and fundamental constructions of combinatorial mathematics
BI Wissenschaftsverlag

László Babai
Almost all Steiner triple systems are asymmetric
Annals of Discrete Mathematics, 37–39, 1980

Charles C Lindner and Alexander Rosa
Steiner quadruple systems-a survey
Discrete Mathematics 22(2), 147–181, 1978

Jean Doyen and Richard M Wilson
Embeddings of Steiner triple systems
Discrete Mathematics 5(3), 229–239, 1973

Dwijendra K Ray-Chaudhuri and Richard M Wilson
Solution of Kirkman’s schoolgirl problem
Proc. Symp. Pure Math, 187–203, 1971

Marshall Hall
Automorphisms of Steiner triple systems
IBM Journal of Research and Development 4(5), 460–472, 1960