Block-transitive 3-(v,4,λ) designs with sporadic or alternating socle.

This paper is a contribution to the classification of block-transitive 3-designs. Let D = (P , B) be a nontrivial 3- (v , 4 , λ) design and G ≤ A u t (D) acts block-transitively on D with sporadic or alternating socle, then there are exactly 6 incomplete designs as follows: D is isomorphic to a 3- (12 , 4 , λ) design with λ ∈ { 3 , 6 } , and G ≅ M 11 ; D is isomorphic to a 3- (22 , 4 , λ) design with λ ∈ { 3 , 16 } , and S o c (G) = M 22 ; D is isomorphic to a 3-(10, 4, 1) design, and G ≅ M 10 , P G L 2 (9) or P Γ L 2 (9) ; D is isomorphic to a 3-(10, 4, 6) design, and S o c (G) = A 6 . [ABSTRACT FROM AUTHOR]