U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with <i>m</i>= 4, 5 and 7 Associated Classes

作     者：Imane Rezgui Zebida Gheribi-Aoulmi Hervé Monod 

作者机构：Department of Mathematics University of Constantine 1 Constantine Algeria INRA UR MaIAGE Jouy-en-Josas Paris France 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2015年第6卷第2期

页      码：242-264页

摘      要：The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).

主 题 词：Association Scheme Combinatory Method (s) Resolvable Partially Balanced Incomplete Block Design U-Type Design 

学科分类：07[理学] 0701[理学-数学类] 070101[070101] 

D　O　I：10.4236/am.2015.62024

馆 藏 号：203219551...