Premium
Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5
Author(s) -
Cusack C. A.,
Graham S. W.,
Kreher D. L.
Publication year - 1995
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.3180030207
Subject(s) - psl , mathematics , combinatorics , block (permutation group theory) , line (geometry) , element (criminal law) , projective line , mod , set (abstract data type) , projective test , discrete mathematics , projective space , geometry , pure mathematics , computer science , political science , law , programming language
We determine the distribution of 3−( q + 1, k ,λ) designs, with k ϵ {4,5}, among the orbits of k ‐element subsets under the action of PSL(2, q ), for q ϵ 3 (mod 4), on the projective line. As a consequence, we give necessary and sufficient conditions for the existence of a uniformly‐PSL(2, q ) large set of 3−( q + 1, k ,λ) designs, with k ϵ {4,5} and q ≡ 3 (mod 4). © 1995 John Wiley & Sons, Inc.