The 3-way intersection problem for S(2,4, v) Designs

Abstract

In this paper the 3-way intersection problem for 5(2,4, v) designs is investigated. Let bv = v(v+1) = {0,1,... ,bv} \ (bv - 7,bv -6,bv- 5,bv -4,bv - 3,bv - 2,bv - 1}. Let J3[v] = I3[v] there exist three 5(2,4, v) designs with k same common blocks}. We show that J3 [v] ⊆ I3[v] for any positive integer v = 1,4 (mod 12) and J3[v] ⊆ [i>], for v ≥ 49 and v = 13. We find J3[16] completely. Also we determine some values of Jafv] for v - 25,28,37 and 40.