Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5

摘要

AbstractWe determine the distribution of 3−(q+ 1,k,λ) designs, withkϵ {4,5}, among the orbits ofk‐element subsets under the action of PSL(2,q), forqϵ 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, withkϵ {4,5} andq≡ 3 (mod 4). © 1995 John