On the construction of orthogonal F-squares of order n from an orthogonal array (n, k, s, 2) and an OL(s, t) set |
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Authors: | John P Mandeli F-CHelen Lee Walter T Federer |
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Institution: | Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA 23284, USA;Biometrics Unit, Cornell University, Ithaca, NY 14853, USA |
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Abstract: | Complete sets of orthogonal F-squares of order n = sp, 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 = 2sp, 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, λ1), F(n, λ2), …, F(n, λ1) squares is given. |
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Keywords: | 62K99 05B15 Complete Sets Asympotically Complete Best Upper Bound Maximal Number Varying Number of Symbols |
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