| Popis: |
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2^nu^1 (HSOLSSOM(2^nu^1)). For u>=2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n>=3u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n= =3u/2+1 or (2) n>=263 and n>=2(u-2). In this paper we show that in (1) the condition n= =263 can be improved to n>=4, except possibly for 19 pairs (n,u), the largest of which is (53,28). |
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