Some new HSOLSSOMs of types hn and 1m u1

✍ Scribed by G. Ge; R. J. R. Abel

• Book ID: 102307467
• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 129 KB
• Volume: 9
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.1022

✦ Synopsis

Abstract

In this paper, two new direct construction methods are given for holey self‐orthogonal Latin squares with a symmetric orthogonal mate (HSOLSSOMs). Some new HSOLSSOMs using already known methods are also given. The known existence results for HSOLSSOMs of types 1^m^ u^1^ and h^n^ are improved; for type 1^m^ u^1^ there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type h^n^, there are just two possible exceptions remaining, for (h, n) = (6, 12) and (6, 18). As a byproduct, the known existence results for three holey mutually orthogonal Latin squares (3 HMOLS) are also improved. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 435–444, 2001