Combinatorial framework of statistical designs and its interface between different area

这是一个为期3年的研究项目，今年是最后一年。在此期间所做的活动总结如下。本项目的研究成果在多个会议（包括统计学和组合学的国际会议）上发表，与其他研究人员进行交流，并得到了许多积极的评价或建议。在日本，这些会议是在京都大学、Kurashilki国际自然科学研究所、埼玉大学、神户大学、庆应义塾大学、东北大学、西原市、上山市组织的，而在日本以外，在澳大利亚布里斯班、葡萄牙托马尔和斯洛伐克布拉迪斯拉发组织的。其中大部分是作为特邀论文发表的。通过这些经验，我们获得了许多有用和富有成效的意见或信息，以进一步发展我们的项目。下面描述了我们的一些主要结果。获得了下列类型的块设计和组合结构的一些构造方法：BIB设计、组可分设计、比较实验双列杂交、矩形设计、差异族设计、三角形设计、分数析因设计、3-设计、分块设计、平衡处理块设计、正交阵列。此外，本文还讨论了仿射α-可解块设计的存在性问题，并取得了一些成果。从方差分析的角度出发，考虑了部分析因设计的统计分析。我们研究了代码结构之间的组合接口，并得到了一些结果。

This is a 3-year research project and this year is final The activity done for the period is summarized as follows.Research results on this project were presented in many conferences (including international conferences on statistics and combinatorics) to communicate with other researchers and then we have received many positive comments or suggestions. Such conferences and meetings are organized, in Japan, at Kyoto Univ., International Institute of Natural Science in Kurashilki, Saitama Univ., Kobe Univ., Keio Univ., Tohoku Univ., Asihara City, Ueyama City, while, outside Japan, at Brisbane in Australia, Tomar in Portugal, and Bratislava in Slovakia. Most of them are presented as invited papers. We have obtained many useful and fruitful comments or information to develop our project further through such experience.Some of our main results are described below.1. Some methods of construction are obtained for the following classes of block designs and combinatorial structures: BIB designs, group divisible designs, diallel crosses for comparative experiments, rectangular designs, difference families, triangular designs, fractionally factorial designs, 3-designs, split-block designs, balanced treatment block designs, orthogonal arrays. Also, the existence problem of affine α-resolvable block designs has been discussed with some fruitful results.2. From a view of point on analysis of valiance, the statistical analysis of fractionally factorial designs are considered with some constructions.3. We study a combinatorial interface between code constructions and some results are obtained.