On the existence of orthogonal designs
نویسندگان
چکیده
منابع مشابه
The asymptotic existence of orthogonal designs
Given any -tuple ( s1, s2, . . . , s ) of positive integers, there is an integer N = N ( s1, s2, . . . , s ) such that an orthogonal design of order 2 ( s1 + s2 + · · ·+ s ) and type ( 2s1, 2 s2, . . . , 2 s ) 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 are all highly divisible by 2, then there is a ful...
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In [5] Raghavarao showed that if n = 2 (mod 4) and A is a {O, 1, -1} matrix satisfying AAt = (n 1) In. then n 1 = a2 b2 for a, b integers. In [4] van Lint and Seidel giving a proof modeled on a proof of the Witt cancellation theorem, proved more generally that if n is as above and A is a rational matrix satisfying AAt = kIn then k = q12 + q22 (q1, q2 E Q, the rational numbers). Consequently, if...
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A nested orthogonal array is an OA(N, k, s, g)which contains an OA(M, k, r, g) as a subarray. Here r < s andM<N . Necessary conditions for the existence of such arrays are obtained in the form of upper bounds on k, given N,M, s, r and g. Examples are given to show that these bounds are quite powerful in proving nonexistence. The link with incomplete orthogonal arrays is also indicated. © 2007 E...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1978
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700007942