| 史册,蒋领,闻斌.单纯正交表OA$_\lambda(3, 5, v)$的存在性[J].数学研究及应用,2015,35(3):271~278 |
| 单纯正交表OA$_\lambda(3, 5, v)$的存在性 |
| Existence of Simple OA$_\lambda(3, 5, v)'$s |
| 投稿时间：2014-05-19 修订日期：2015-03-04 |
| DOI：10.3770/j.issn:2095-2651.2015.03.004 |
| 中文关键词: 正交表 单纯的 构造 存在性 |
| 英文关键词:orthogonal arrays simple construction existence |
| 基金项目:国家自然科学基金项目(Grant Nos.11301342; 11226282),上海高校青年教师培养资助计划项目(Grant No.ZZlx13001). |
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| 中文摘要: |
| 正交表是一个$\lambda v^t\times k$阵列, 每列上的元素取自一个$v$元符号集, 且满足每个$\lambda v^t\times t$子阵列包含每个$t$-元组恰好$\lambda$次, 记为OA$_\lambda(t,k,v)$, 其中$t$为强度, $k$为度, $v$为阶数, $\lambda$为指标. 一个正交表OA$_\lambda(t,k,v)$称为单纯的, 如果它不含有重复的行向量, 用SOA$_\lambda(t,k,v)$来表示. 本文证明了除去$v=6$和$\lambda \in \{3,7,11,13,15,17,19, 21,23,25,29,33\}$可能的例外, 单纯正交表SOA$_\lambda(3,5,v)$存在的必要条件也是充分的, 其中$\lambda \geq 2$. |
| 英文摘要: |
| An orthogonal array of strength $t$, degree $k$, order $v$ and index $\lambda$, denoted by OA$_\lambda(t,k,v)$, is a $\lambda v^t\times k$ array on a $v$ symbol set such that each $\lambda v^t\times t$ subarray contains each $t$-tuple exactly $\lambda$ times. An OA$_\lambda(t,k,v)$ is called simple and denoted by SOA$_\lambda(t,k,v)$ if it contains no repeated rows. In this paper, it is proved that the necessary conditions for the existence of an SOA$_\lambda(3,5,v)$ with $\lambda \geq 2$ are also sufficient with possible exceptions where $v=6$ and $\lambda \in \{3,7,11,13,15,17,19, 21,23,25,29,33\}$. |
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