区组大小为5的不完全横截设计的存在性(英文)

Existence of Incomplete Transversal Designs with Block Size Five

摘要: 除１０６个有序数对（ｖ，ｎ）作为可能的例外，区组大小为５的不完全横截设计ＴＤ（５，ｖ）－ＴＤ（５，ｎ）存在的充分必要条件是ｖ≥４ｎ。本文对１０６种可能的例外中的１２种情况，给出ＴＤ（５，ｖ）－ＴＤ（５，ｎ）的存在性证明。

Abstract: It has been shown that incomplete transversal designs with block size five,TD(5, v )-TD(5, n), exist if and only if v ≥ 4n,with 106 ordered pairs ( v ,n) as possible exceptions.In this paper,we give the existence of TD(5, v )-TD(5,n) for twelve of the possible exceptions.