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Some new HSOLSSOMs of types h n and 1 m u 1
Author(s) -
Ge G.,
Abel R. J. R.
Publication year - 2001
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.1022
Subject(s) - combinatorics , latin square , mathematics , type (biology) , orthogonal array , physics , statistics , chemistry , ecology , rumen , food science , taguchi methods , fermentation , biology
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