Premium
Existence of strong difference families and constructions for eight new 2‐designs
Author(s) -
Wang Xiaomiao,
Feng Tao,
Wang Shixin
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21765
Subject(s) - mathematics , abelian group , block (permutation group theory) , combinatorics , significant difference , block design , difference set , base (topology) , pure mathematics , statistics , mathematical analysis
Abstract Using group rings and characters as in the theory of abelian difference sets, some nonexistence results for strong difference families are provided. Existences of strong difference families with base block size 3 ≤ k ≤ 9 are discussed. Via strong difference families, eight 2‐ ( v , k , λ ) designs whose existences were unknown are constructed for ( v , k , λ ) ∈ { ( 3417 , 8 , 1 ) , ( 3753 , 8 , 1 ) , ( 2665 , 9 , 1 ) , ( 3817 , 9 , 1 ) , ( 4393 , 9 , 1 ) , ( 7353 , 9 , 1 ) , ( 12537 , 9 , 1 ) , ( 345 , 9 , 3 ) } .