A Kirkman square of order 51 and block size 3
暂无分享,去创建一个
A necessary condition for the existence of a Kirkman square KS 3 ( v ) is v ≡ 3 (mod 6). It is known that for all v sufficiently large and v ≡ 3 (mod 6) that such a design exists. In order to settle the existence question completely a number of small designs must be constructed directly. Of the 14 possible orders less than 100 only 4 are currently known to exist. In this paper we establish the existence of one more design with order less than 100; namely, v = 51.
[1] Douglas R. Stinson,et al. On strong starters in cyclic groups , 1985, Discret. Math..
[2] W. D. Wallis,et al. The existence of Room squares , 1975 .
[3] S. A. VANSTONE,et al. Doubly resolvable designs , 1980, Discret. Math..
[4] Alexander Rosa,et al. On the Existence of Strong Kirkman Cubes of Order 39 and Block Size 3 , 1985 .