| Research Abstract |
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.
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