A method of constructing 2-resolvable t-designs for t=3,4

• Published in: Designs, codes, and cryptography Vol. 90; no. 7; pp. 1567 - 1583
• Main Author: van Trung, Tran
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2022; Springer Nature B.V
• Subjects: Coding and Information Theory; Computer Science; Cryptology; Discrete Mathematics in Computer Science; Infinite series; resolvable; Projective plane; design; Steiner 2-design; 05B05
• ISSN: 0925-1022; 1573-7586
• DOI: 10.1007/s10623-022-01056-w

The paper introduces a method for constructing 2-resolvable t -designs for 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 , 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 resolution classes with parameters 5- ( 14 + 8 m , 7 , 10 ( 9 + 8 m ) ( 1 + m ) ) for any 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.