## Abstract

Complete sets of orthogonal F-squares of order n = s^{p}, where g is a prime or prime power and p is a positive integer have been constructed by Hedayat, Raghavarao, and Seiden (1975). Federer (1977) has constructed complete sets of orthogonal F-squares of order n = 4t, where t is a positive integer. We give a general procedure for constructing orthogonal F-squares of order n from an orthogonal array (n, k, s, 2) and an OL(s, t) set, where n is not necessarily a prime or prime power. In particular, we show how to construct sets of orthogonal F-squares of order n = 2s^{p}, where s is a prime or prime power and p is a positive integer. These sets are shown to be near complete and approach complete sets as s and/or p become large. We have also shown how to construct orthogonal arrays by these methods. In addition, the best upper bound on the number t of orthogonal F(n, λ_{1}), F(n, λ_{2}), ..., F(n, λ_{1}) squares is given.

Original language | English |
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Pages (from-to) | 267-272 |

Number of pages | 6 |

Journal | Journal of Statistical Planning and Inference |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - 1981 |

Externally published | Yes |

## Keywords

- Asympotically Complete
- Best Upper Bound
- Complete Sets
- Maximal Number
- Varying Number of Symbols