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Holey Schröder designs of type 2nu1

✍ Scribed by F. E. Bennett; Ruizhong Wei; Hantao Zhang

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
283 KB
Volume
6
Category
Article
ISSN
1063-8539

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✦ Synopsis

A holey Schröder design of type h n

] of order m with ni missing subquasigroups (holes) of order hi, 1 ≤ i ≤ k, which are disjoint and spanning, that is, 1 ≤i≤k nihi = m. In this article, we first consider the existence of HSD(2 n u 1 ) for 1 ≤ u ≤ 4 and show that these HSDs exist if and only if n ≥ u + 1 with the exception of (n, u) ∈ {(2, 1), (3, 1), (3, 2)}. Then we investigate the existence of HSD(2 n u 1 ) for general u and prove that there exists an HSD(2 n u 1 ) for u ≥ 16 and n ≥ [5u/4] + 14.

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