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Classification of resolvable balanced incomplete block designs — the unitals on 28 points

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Mathematica Slovaca

Abstract

Approaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points.

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Authors and Affiliations

  1. Department of Computer Science Helsinki Institute for Information Technology HIIT, University of Helsinki, P.O. Box 68, 00014, University of Helsinki, Finland

    Petteri Kaski

  2. Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015 TKK, Helsinki, Finland

    Patric R. J. Östergård

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  1. Petteri Kaski
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  2. Patric R. J. Östergård
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Correspondence to Petteri Kaski.

Additional information

(Communicated by Peter Horák)

Dedicated to Alex Rosa on the occasion of his seventieth birthday

This research was supported in part by the Academy of Finland, Grants No. 107493, 110196, and 117499.

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Kaski, P., Östergård, P.R.J. Classification of resolvable balanced incomplete block designs — the unitals on 28 points. Math. Slovaca 59, 121–136 (2009). https://doi.org/10.2478/s12175-009-0113-8

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