1. A method of constructing 2-resolvable t-designs for $$t=3,4$$
- Author
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van Trung, Tran
- Subjects
Applied Mathematics ,Mathematik ,Computer Science Applications - Abstract
The paper introduces a method for constructing 2-resolvable t-designs for $$t=3,4$$ t = 3 , 4 . The main idea is based on the assumption that there exists a partition of a t-design into Steiner 2-designs. A remarkable property of the method is that it enables the construction of 2-resolvable t-designs with a large variety of block sizes. For $$t=4$$ t = 4 , it is required that the Steiner 2-designs of the partition are projective planes and this case would also lead to a construction of 3-resolvable 5-designs. For instance, we show the existence of an infinite series of 3-resolvable 5-designs having $$N=5$$ N = 5 resolution classes with parameters 5-$$(14+8m,7, 10(9+8m)(1+m))$$ ( 14 + 8 m , 7 , 10 ( 9 + 8 m ) ( 1 + m ) ) for any $$m \ge 0$$ m ≥ 0 as a byproduct. Moreover, it turns out that the method is very effective, as it yields infinitely many 2-resolvable 3-designs. However, the question of simplicity of the constructed designs has not been yet investigated.
- Published
- 2022
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