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Helsinki University of Technology, 
     Laboratory for Theoretical Computer Science

Enumeration of balanced ternary designs


Petteri Kaski and Patric R. J. Östergård. Enumeration of balanced ternary designs. Discrete Applied Mathematics, 138(1–2):133–141, 2004.


A balanced ternary design is a pair , where is a -set of points and is a collection of -multisubsets of called blocks, such that each point appears times in the blocks and no block contains a point with multiplicity greater than two. Each point must appear in blocks with multiplicity one and in blocks with multiplicity two. Additionally, every pair of distinct points must appear exactly times in the blocks of the design. A backtrack search algorithm with isomorph rejection is described and employed to enumerate the balanced ternary designs with , , and for all but 12 of the 155 possible design classes with these parameters.


balanced ternary design, enumeration, orderly algorithm

Suggested BibTeX entry:

    author = {Petteri Kaski and Patric R. J. {\"O}sterg{\aa}rd},
    journal = {Discrete Applied Mathematics},
    number = {1--2},
    pages = {133--141},
    title = {Enumeration of balanced ternary designs},
    volume = {138},
    year = {2004},

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