NOTE ON REGULAR D-OPTIMAL MATRICES

作     者：LI QIAOLIANG Department of Mathematics, Hunan Normal University, Changsha 410081, China. Center for Combinatorics, Nankai University, Tianjin 300071, China. E-mail: liqiaoliang@*** 

作者机构：Department of Mathematics Hunan Normal University Changsha 410081 China Center for Combinatorics Nankai University Tianjin 300071 China 

基　　金：Project supported by the Science Foundation of China for Postdoctors (No.5(2001)) 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2003年第24卷第2期

页      码：215-220页

摘      要：Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.

主 题 词：Regular .D-optimal matrices Simplex Weighing design 

学科分类：07[理学] 070104[070104] 0701[理学-数学类] 

核心收录：

D　O　I：10.1142/S0252959903000190

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