Given any l-tuple (s1, s2,..., sl) of positive integers, there is an integer N = N (s1, s2,..., sl) such that an orthogonal design of order 2n (s1+s2+...+sl) and type (2ns1, 2ns2,..., 2nsl) exists, for each n ≥ N. This complements a result of Eades et al. which in turn implies that if the positive integers s1, s2,..., s_l are all highly divisible by 2, then there is a full orthogonal design of type (s1, s2,..., sl).
The asymptotic existence of orthogonal designs / Ghaderpour, E.; Kharaghani, H.. - In: TEH AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 1034-4942. - 58:2(2014), pp. 333-346.
The asymptotic existence of orthogonal designs
Ghaderpour E.
;
2014
Abstract
Given any l-tuple (s1, s2,..., sl) of positive integers, there is an integer N = N (s1, s2,..., sl) such that an orthogonal design of order 2n (s1+s2+...+sl) and type (2ns1, 2ns2,..., 2nsl) exists, for each n ≥ N. This complements a result of Eades et al. which in turn implies that if the positive integers s1, s2,..., s_l are all highly divisible by 2, then there is a full orthogonal design of type (s1, s2,..., sl).File allegati a questo prodotto
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