Constructs partially replicated (p-rep) designs in which every treatment occurs in
every location, once or twice in Methods I and III and q or q + 1 times
in Method II, with constant overall replication. Method I
decomposes the complete graph into Hamiltonian paths, Method II uses
cyclic blocks derived from a Hamiltonian cycle, and Method III uses
mutually orthogonal Latin squares over a Galois field. Three
treatment-replacement extensions (block enlargement, block splitting,
and replacement followed by column-wise splitting) can be applied to
Methods I and II. Each design is checked for connectedness and is
returned with its parameters, pairwise concurrence distribution,
canonical efficiency factor (CEF), average variance factor (AVF) and a randomized layout.
Background references:
Vinaykumar et al. (2026)