The number of repeated blocks in balanced ternary designs with block size three II

AbstractLet D denote any balanced ternary design on v elements with block size three, index two, and ϱ2 = 2 (so each element occurs repeated in precisely two blocks). D is thus also a multi-set design MB2(υ, 3, 2), in the terminology of Assaf, Hartman and Mendelsohn.This paper shows that such a design D exists which contains exactly k pairs of repeated blocks if and only if υ ≡ 0 or 2 modulo 3, υ ⩾ 5 and 0 ⩽ k ⩽ tυ = 116υ(υ − 5), k ≠ tυ − 1