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The Geometry of Frequency Squares

✍ Scribed by Dieter Jungnickel; V.C. Mavron; T.P. McDonough

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 122 KB
Volume: 96
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3196

No coin nor oath required. For personal study only.

✦ Synopsis

to professor hanfried lenz on the occasion of his 85th birthday This paper establishes a correspondence between mutually orthogonal frequency squares (MOFS) and nets satisfying an extra property (''framed nets''). In particular, we provide a new proof for the bound on the maximal size of a set of MOFS and obtain a geometric characterisation of the case of equality: necessary and sufficient conditions for the existence of a complete set of MOFS are given in terms of the existence of a certain type of PBIBD based on the L 2 -association scheme. We also discuss examples obtained from classical affine geometry and recursive construction methods for (complete) sets of MOFS.

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