關於一些設計的變型的研究

Abstract

我們進一步探討了由D.F. Hsu所提出的定義在秩為 9 的循環群上的所有 (K,1) 一般完全映射, 利用群的作用來賦予另一種解釋, 並給予些微的修 正. 此外亦建構了一些強或可容許的完全映射, 簡單完全映射以及曼德森 設計. 最後用拉丁陣來建構 3-(v,k,.lambda.) 有序區塊設計族. A complete list of (K,1) generalized complete mappings over the group (Z9,+(mod9)) offered by Hsu is furthered studied; among them, a minor correction is made, another interpretation in terms of group action is given. We also construct some strong or admissible (K,1) complete mappings, simple (K,.lambda.) complete maappings, Mendelsohn designs. Finally, a family of 3-(v,k,.lambda.) ordered block designs is constructed in terms of orthogonal Latin cubes.