Preece, Donald A.,
Vowden, Barry J.
(1999)
*
Some series of cyclic balanced hyper-Graeco-latin superimpositions of three Youden squares.
*
Discrete Mathematics,
198
.
pp. 671-682.
ISSN 0012-365X.
(doi:10.1016/S0012-365X(99)90131-0)
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Official URL http://dx.doi.org/10.1016/S0012-365X(99)90131-0 |

## Abstract

General constructions are provided for some cyclic balanced hyper-Graeco-Latin superimpositions of three Youden squares. These superimpositions are all row-column designs of sizes q x (2q + 1) and (q + 1) x (2q + 1) where 2q + 1 is a prime power congruent to 3 (modulo 4). For 2q + 1 greater than or equal to 11, the designs of each size fall into three combinatorially (and statistically) distinct classes. The basic constructions, which extend constructions by Potthoff (1963) and Agrawal and Sharma (1978), involve systematic use of successive even powers and successive odd powers of a primitive element of GF(2q + 1). However, we illustrate how an idea taken from Preece and Phillips (1997) can be extended to produce some slightly more involved variants of the constructions when q is composite and sufficiently large.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1016/S0012-365X(99)90131-0 |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | F.D. Zabet |

Date Deposited: | 22 Apr 2009 18:17 UTC |

Last Modified: | 10 Jun 2019 10:59 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/16490 (The current URI for this page, for reference purposes) |

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