Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ

被引：19
作者：
Abel R.J.R. [1 ]
Colbourn C.J. [2 ]
Yin J. [3 ]
Zhang H. [4 ]
机构：
[1] School of Mathematics, University of New South Wales, Kensington
[2] Combinatorics and Optimization, University of Waterloo, Waterloo
[3] Department of Mathematics, Suzhou University
[4] Computer Science, University of Iowa, Iowa City
来源：
Designs, Codes and Cryptography | 1997年 / 10卷 / 3期
基金：
加拿大自然科学与工程研究理事会; 美国国家科学基金会;
关键词：
Group divisible design; Latin square; Orthgonal array; Pairwise balanced design; Transversal design;
D O I：
10.1023/A:1008232418845
中图分类号：
学科分类号：
摘要：
The basic necessary condition for the existence of a T D (5, λ; υ) - T D (5, λ; u), namely υ ≥ 4u, is shown to be sufficient for any λ ≥ 1, except when (υ, u) = (6, 1) and λ = 1, and possibly when (υ, u) = (10, 1) or (52, 6) and λ = 1. For the case λ = 1, 86 new incomplete transversal designs are constructed. Several construction techniques are developed, and some new incomplete TDs with block size six and seven are also presented.
引用
收藏
页码：275 / 307
页数：32
相关论文
共 37 条
  • [1] Abel R.J.R., Four mutually orthogonal latin squares of order 28 and 52, J. Combin. Theory (A), 58, pp. 306-309, (1991)
  • [2] Abel R.J.R., On the Existence of Balanced Incomplete Block Designs and Transversal Designs, (1995)
  • [3] Abel R.J.R., Colbourn C.J., Dinitz J.H., Incomplete MOLS: CRC Handbook of Combinatorial Designs, pp. 142-172, (1996)
  • [4] Abel R.J.R., Todorov D.T., Four MOLS of order 20, 30, 38 and 44, J. Combin. Theory (A), 64, pp. 144-148, (1993)
  • [5] Beth T., Jungnickel D., Lenz H., Design Theory, (1986)
  • [6] Bose R.C., Shrikhande S.S., Parker E.T., Further results on the construction of mutually orthogonal latin squares and the falsity of Euler's conjecture, Canad. J. Math., 12, pp. 189-203, (1960)
  • [7] Brouwer A.E., Four MOLS of order 10 with a hole of order 2, J. Statist. Planning and Inference, 10, pp. 203-205, (1984)
  • [8] Brouwer A.E., The number of mutually orthogonal latin squares - A table up to order 10000, Math. Cent. Report ZW 123/79
  • [9] Brouwer A.E., Van Rees G.H.J., More mutually orthogonal latin squares, Discrete Math., 39, pp. 263-281, (1982)
  • [10] Colbourn C.J., Four MOLS of order 26, J. Comb. Math. Comb. Comput., 17, pp. 147-148, (1995)
1234