Direct constructions for certain types of HMOLS
type: Item
instance of: scholarly article
title: Direct constructions for certain types of HMOLS
zbMATH Open document ID: 0911.05020
DOI: 10.1016/S0012-365X(97)00021-6
author: R. Julian R. Abel
author: Hantao Zhang
published in: Discrete Mathematics
publication date: 1999-05-04T00:00:00Z
review text: The authors give direct constructions for 16 new orders of 3-HMOLS, 7 orders of 4-HMOLS, 2 orders of 6-HMOLS, 34 orders of 7-HMOLS all with equal sized holes. In addition, they give constructions for 4 new orders of 3-HMOLS of type \((2^n3^1)\) and 7 new orders of 4-HMOLS of type \((2^n3^1)\). Prior results plus some of the results of this paper can be summarized as follows: (1) if \(n\geq 5\), then there exist 3-HMOLS of type \(h^n\), except for \((h,n)=(1,6)\) and possibly for \((h,n)\in \{(1,10), (3,6), (3, 18), (3,28),(3,34),(6,18),(6,19),(6,23)\}\), (2) there exist 7-HMOLS of type \(3^p\) for all primes \(p\equiv 1\) \(\pmod 6\), with \(30< p<400\), and (3) there exist 3-HMOLS of type \((2^n3^1)\) for all \(n \geq 6\) except possibly for \(n\in\{6,9,10, 12,14,15,17, 21,24,26, 27\}\).
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1135953
reviewed by: J. H. Dinitz
MaRDI profile type: Publication
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full work available at URL: s0012-365x(97)00021-6
OpenAlex ID: W1995506984
description: scientific article; zbMATH DE number 1135953