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An extending theorem for s-resolvable t-designs
Designs, Codes and Cryptography ( IF 1.4 ) Pub Date : 2021-01-17 , DOI: 10.1007/s10623-020-00835-7
Tran van Trung

An extending theorem for s -resolvable t -designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s -resolvable t -designs, and mutually disjoint t -designs. For example, it can be shown that if there exists a large set LS [29](4, 5, 33), then there exists a family of 3-resolvable 4- $$(5+29m, 6, \frac{5}{2}m(1+29m) )$$ ( 5 + 29 m , 6 , 5 2 m ( 1 + 29 m ) ) designs for $$m \ge 1,$$ m ≥ 1 , with 5 resolution classes. Moreover, for any given integer $$h \ge 1$$ h ≥ 1 , there exist $$(5\cdot 2^h-5)$$ ( 5 · 2 h - 5 ) mutually disjoint simple 3- $$(3+m(5\cdot 2^h-3),4,m)$$ ( 3 + m ( 5 · 2 h - 3 ) , 4 , m ) designs for all $$m \ge 1.$$ m ≥ 1 . In addition, we give a brief account of t -designs derived from the result of Wu.

中文翻译:

s 可解析 t 设计的扩展定理

提出了 s 可解析 t 设计的扩展定理,可以将其视为吴秋荣结果的扩展。该定理为 s 可解析 t 设计和互不相交的 t 设计产生递归构造。例如,可以证明如果存在一个大集合 LS [29](4, 5, 33),那么存在一个 3-resolvable 4- $$(5+29m, 6, \frac{5 }{2}m(1+29m) )$$ ( 5 + 29 m , 6 , 5 2 m ( 1 + 29 m ) ) 设计为 $$m \ge 1,$$ m ≥ 1 ,具有 5 个分辨率等级. 此外,对于任何给定的整数 $$h \ge 1$$ h ≥ 1 ,存在 $$(5\cdot 2^h-5)$$ ( 5 · 2 h - 5 ) 互不相交的简单 3- $$( 3+m(5\cdot 2^h-3),4,m)$$ ( 3 + m ( 5 · 2 h - 3 ) , 4 , m ) 所有 $$m \ge 1.$$ m 设计≥ 1 。此外,我们还简要介绍了从 Wu 的结果中导出的 t 设计。
更新日期:2021-01-17
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