The Geometry of Frequency Squares

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6 Citations (SciVal)

Abstract

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 L2-association scheme. We also discuss examples obtained from classical affine geometry and recursive construction methods for (complete) sets of MOFS.
Original languageEnglish
Pages (from-to)376-387
Number of pages12
JournalJournal of Combinatorial Theory, Series A
Volume96
Issue number2
DOIs
Publication statusPublished - Nov 2001

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