【摘要】：正交表在人類研究的各個(gè)領(lǐng)域都非常重要,其定義簡單,目前已有多種構(gòu)造方法.但為實(shí)際的應(yīng)用構(gòu)造特定的正交表仍是一個(gè)值得深入研究的課題.本文運(yùn)用圓柱拉丁方和替代法構(gòu)造一系列強(qiáng)度為3的非對稱正交表.Nguyen(2008)采用拉丁方從互補(bǔ)對網(wǎng)格出發(fā),構(gòu)造強(qiáng)度為3,試驗(yàn)次數(shù)是96的非對稱正交表OA(96,6×4~2×2~k,3),1≤k≤5.本文在第二章中提出列互補(bǔ)對概念,從列互補(bǔ)對出發(fā)構(gòu)造非對稱正交表OA(96,6×4~2×2~k,3),k≤3.這些相關(guān)的理論結(jié)果更加一般化.在此基礎(chǔ)上,本文進(jìn)一步找到非對稱正交表OA(96,6×4~2×2~5,3)的存在結(jié)果.Suen et al.(2001)提出一種因子水平s是2的冪次的替代法.即從對稱正交表出發(fā),經(jīng)過一系列替換步驟構(gòu)造強(qiáng)度為3,試驗(yàn)次數(shù)是2s3的緊的非對稱正交表.本文在第三章中,我們將這種替代法推廣到一般形式,即從正交表OA(s~m,n,(s~r)×s~(n-1),3)(s=pk,p是素?cái)?shù),k是整數(shù))出發(fā),經(jīng)過一系列替換步驟得到非對稱正交表OA(ps~m,n,(ps~r)×s~(n-1),3),然后將一個(gè)pk-水平因子用一些p-水平因子替換,得到一系列非對稱正交表OA(ps~m,t+u+1,(ps~r)×s~t×p~u,3),t,u是整數(shù).這種替代法不影響正交表的正交性.本文主要考慮p=2,3的情況,得到一系列新的非對稱正交表,其中有一些結(jié)果是緊的.本文在最后還討論了一個(gè)3k-水平因子用3-水平因子替換的個(gè)數(shù)問題.
[Abstract]:Orthogonal table is very important in all fields of human research, and its definition is simple. However, the construction of specific orthogonal tables for practical applications is still a subject worthy of further study. In this paper, a series of asymmetric orthogonal tables with strength of 3 (. Nguyen (2008) are constructed by means of cylindrical Latin square and substitution method. Using Latin square, starting from complementary pairs of grids, the construction strength is 3 and the number of experiments is 96. The asymmetric orthogonal table OA (96 ~ 6 脳 4 ~ 2 脳 2 ~ 2 脳 2 ~ (2) K ~ (3), 1 鈮，

本文編號(hào)：2267826