论文信息 - Some new HSOLSSOMs of types hn and 1m u1

Some new HSOLSSOMs of types hn and 1m u1

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 1mu1 and hn are improved; for type 1mu1 there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type hn, 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

Gennian Ge | R. J. R. Abel

[1] Douglas R. Stinson,et al. On the spectrum of resolvable orthogonal arrays invariant under the Klein group K4 , 1983 .

[2] Y. Lu,et al. Existence of whist tournaments with the three-person property 3PWh(v) , 2000, Discret. Appl. Math..

[3] Gennian Ge,et al. Authentication perpendicular arrays APA1(2, 5, v) , 1996 .

[4] Gennian Ge. Uniform frames with block size four and index one or three , 2001 .

[5] R. Julian R. Abel,et al. Direct constructions for certain types of HMOLS , 1998, Discret. Math..

[6] Frank E. Bennett,et al. Holey self-orthogonal Latin squares with symmetric orthogonal mates , 1997 .

[7] Douglas R. Stinson,et al. Steiner pentagon systems , 1984, Discret. Math..

[8] Frank E. Bennett,et al. Holey Steiner pentagon systems , 1999 .

[9] Lie Zhu,et al. The spectrum of HSOLSSOM(hn) where h is even , 1996, Discret. Math..