Block disjoint difference families for Steiner triple systems:

Constructions of External Difference Families and Disjoint Difference Families

“…In the case g = 1 or H = {0}, we write a (G, H, k, λ)-DDF briefly as a (G, k, λ)-DDF (or (v, k, λ)-DDF over G). The (G, k, λ)-DDFs have been investigated intensively (see, e.g., [9][10][11]24]). …”

Two new infinite families of extremal class‐uniformly resolvable designs

“…Proof. From [5], there exists a cyclic Steiner triple system on n points with the property that the base blocks are all disjoint. Let B be the set of base blocks in such a system.…”

“…{3, 7, 10}} and B = {{∞ 1 , 0, 2}, {∞ 2 , 6, 8}}. It is easy to check that the set of blocks {A+ i |, 0 ≤ i ≤ 15} ∪ {B + i | i = 0,1,4,5,8,9, 12, 13} is indeed a class-disjoint 3-GDD of type 29 .…”

Two constructions of (v, (v − 1)/2, (v − 3)/2) difference families

“…Difference families are well studied and have applications in coding theory and cryptography [3,4,[8][9][10]15].…”