The geometry of frequency squares

摘要

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. (C) 2001 Academic Press. [References: 18]