本作者一组有关弱相关试验设计之超立方的博客链接，点击即可浏览。 学习极值原理 回归试验设计的质量要素 弱相关试验设计（修订） 介绍正交超立方试验设计表 正交超立方设计的命名约定 用张量积构造正交超立方存在的缺陷 修正一处认识 同 C.D.Lin 等四博士讨论堆叠法构造正交超立方设计问题 同 C.D.Lin 等四博士讨论堆叠法构造正交超立方设计问题(续1) 同 C.D.Lin

一类试验设计表的命名约定 w17h6o w18h0o w19h7o w20h6o w21h7o w22h0o w23h7o w24h7o w25h7o w26h0o w27h6o w28h7o w29h6o w30h0o w31h6o w32h60 w33h5o w34h0o w35h6o w36h6o w37h6o

W36h6o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 13,22,26,12,07,05,14,05,03,11,29,04,18,12,21,08,23,12,02,09,03,33,04, 34,14,03,28,14,16,34,29,04,10,33,07,25,18,01,16,07,03,24,14,02,10,20,

W35h6o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 20,22,12,33,07,31,23,19,07,02,22,14,15,08,26,09,35,01,34,35,28,21,13, 21,21,32,22,23,16,03,34,11,18,35,35,35,31,06,32,29,32,31,31,18,28,35,

W34h0o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 29,19,28,26,34,02,28,03,20,26,30,04,33,30,12,12,25,30,11,12,27,29,03, 27,25,10,19,14,17,05,33,30,34,04,02,28,08,17,16,04,01,20,11,32,12,12,

W33h5o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 18,29,23,10,26,11,18,06,16,23,22,01,19,24,02,33,27,10,32,31,12,29,25, 27,03,12,11,09,14,28,31,30,32,31,11,30,04,10,27,29,31,11,14,18,10,22,

W32h6o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 02,04,09,18,10,20,03,09,20,07,05,05,28,29,06,30,08,21,05,11,29,19,29, 10,27,19,30,32,10,24,11,07,01,08,26,10,31,15,01,10,28,18,09,10,26,16,

W31h6o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 09,29,16,15,18,17,03,18,29,28,30,26,12,15,11,08,26,05,09,04,19,01,26, 16,30,05,13,07,28,06,09,17,02,16,02,01,14,10,25,17,29,23,24,09,05,14,

W30h0o Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 02,02,09,12,08,13,07,30,24,11,12,23,12,13,12,30,13,25,21,01,22,15,24, 15,19,19,27,29,06,20,05,21,13,29,29,26,02,14,09,04,29,06,11,06,10,08,

W29h6 Author : He Shenze (Email：heshenze@gmail.com ) Columns 1 to 23 20,09,09,05,26,23,22,24,16,08,02,01,11,29,04,14,17,19,06,19,26,02,10, 05,29,23,20,15,29,03,29,14,17,11,24,23,26,26,05,27,08,04,21,12,12,13,

W26H0o Author : He Shenze (Email：heshenze@gmail.com ) 17,18,08,26,22,24,16,25,05,11,19,08,24,23,20,13,11,18,14,01,23,20,17,13,02, 21,13,07,11,15,12,11,15,16,03,01,26,23,01,24,06,21,01,11,17,20,24,10,17,13,

W18H0o Author : He Shenze (Email：heshenze@gmail.com ) 03,18,14,15,03,16,12,18,13,16,06,06,11,07,07,14,13, 18,09,01,16,07,07,14,02,12,13,04,01,10,06,11,15,03, 05,12,18,12,08,05,05,05,01,03,14,03,12,10,16,17,08,

W17H6o Author : He Shenze (Email：heshenze@gmail.com ) 07,05,09,02,10,17,16,12,07,16,10,13,02,02,14,10, 11,02,10,04,11,09,05,08,04,02,13,10,03,14,03,01, 17,10,02,08,14,16,08,15,10,01,03,12,15,09,12,09,

贺深泽 (Email：heshenze@gmail.com ) 整理说明 本文原稿独立作于2005年，发表于《数学的实践与认识》（Vol.39，No. 3, 99-107）。 经查，零相关与弱相关试验设计的概念与国际上一些数学家的 orthogonal Latin hypercube 及 nearly orthogonal Latin hypercube

W22H0o Author : He Shenze 08,10,11,04,06,20,20,22,07,04,17,19,02,16,06,03,07,09,04,18,05, 16,02,13,08,21,13,22,19,12,22,08,09,09,06,09,18,20,21,10,19,20,

附录：堆叠法 贺深泽 (Email：heshenze@gmail.com ) 1. 前言 Lin 堆叠法的基本功能是从现有较小运行数的正交超立方构造出较大的正交超立方（OHC）。 本文遵循 Lin 的思路，但从正交阵列的可堆叠性质出发，推导出真正基于堆叠模型的方法。 正交超立方的构造是一类 NP Hard 难题，十分困难。随着运行数 n 的增加，构造难度迅速地增加。 置换集 S

W20H6o Author : He Shenze 09,12,10,20,19,08,05,08,15,07,08,14,08,08,14,19,18,01,18, 15,01,15,11,11,02,10,02,03,17,11,04,02,14,08,08,20,15,11, 18,16,17,04,06,10,20,03,10,01,13,19,05,06,09,16,11,07,04,

贺深泽 (Email：heshenze@gmail.com ) 5. 关于定理 2 5.1 定理的表述 Lin's Theorem 2. There exists an orthogonal Latin hypercube of n≥4 runs with more than one factor if and only if n ≠ 4k +2 for any integer k.

贺深泽 (Email：heshenze@gmail.com ) 3. 堆叠法构造 OLHD 3.1 Lin 的堆叠法导言 作者不论证OLHD 的可堆叠性，从定理 1 导出了两个堆叠法。这样操作得到的一定是 OLHD 不需要证明？ 是不是满足这一条件就一定能得到 OLHD？而且“ Da and Da themselves are not necessarily Latin hypercubes.” 我不敢相信。

贺深泽 (Email：heshenze@gmail.com ) 2.3 Lin 的定理 1 Let γ=n2. Then design L in (2.1) is an orthogonal Latin hypercube if: (i). A and D are orthogonal matrices of ±1, (ii). Both B and C are orthogonal