具有四元块且类型为 g^u m^1 的群可除设计——III
摘要
我们研究块大小为 4、群类型为 g^u m^1 的群可除设计，其中 g ≡ 2 或 4 (mod 6)。我们证明了当 g = 14, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 58, 62, 68, 76, 88, 92, 100, 104, 116, 124, 136, 152, 160, 176, 184, 200, 208, 224, 232, 248, 272, 304, 320, 368, 400, 448, 464 和 496 时，存在类型为 g^u m^1 的 4-GDD 的必要条件也是充分的。利用这些结果，我们进一步证明了当 g = 2^t q^s，q = 19, 23, 25, 29, 31，s, t = 1, 2, ...，以及 g = 2^t q，q = 2, 5, 7, 11, 13, 17，t = 1, 2, ... 时必要条件也是充分的，仅对少数较大的 m 值可能存在例外 56^9 m^1、80^9 m^1 和 112^9 m^1。
引用
@article{arxiv.1903.07064,
title = {Group divisible designs with block size four and type g^u m^1 - III},
author = {Anthony D. Forbes},
journal= {arXiv preprint arXiv:1903.07064},
year = {2019}
}
备注
128 pages, including 107-page Appendix. This is the third of three papers dealing with 4-GDDs of type g^u m^1. To make the paper self-contained we have included material from arXiv:1806.07491. However, the main results are distinct from those of arXiv:1806.07491. An abridged version will be submitted to a journal