Combinatorial framework of statistical designs and its interface between different area

这是一个为期三年的研究项目，今年是最后一年。在此期间所做的活动总结如下：该项目的研究成果在许多会议上（包括统计学和组合学的国际会议）与其他研究人员进行交流，然后我们收到了许多积极的意见或建议。在日本的京都大学，琦玉大学国际自然科学研究所科比大学，庆应义塾大学东北大学，在日本以外的澳大利亚布里斯班、葡萄牙的托马尔和斯洛伐克的布拉迪斯拉发。其中大多数是作为特邀论文提交的。通过这些经验，我们获得了许多有用的和富有成效的意见或信息，以进一步发展我们的项目。给出了下列几类区组设计和组合结构的构造方法：BIB设计、可分组设计、比较试验的双列杂交、矩形设计、差族、三角形设计、部分因子设计、3-设计、裂区设计、平衡处理区组设计、正交表。并讨论了仿射α-可分解区组设计的存在性问题，得到了一些有意义的结果.从方差分析的角度出发，对部分析因设计的统计分析进行了讨论.我们研究了码构造之间的组合接口，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.