Abstract:
Construction of Balanced Incomplete Block Designs (BIBD) is a combination problem that involves the
arrangement of 𝑣 treatments into 𝑏 blocks each of size 𝑘 such that each treatment is replicated exactly 𝑟 times
in the design and a pair of treatments occur together in 𝜆 blocks. Several methods of constructing BIBDs
exist. However, these methods still cannot be used to design all BIBDs. Therefore, several BIBDs are still
unknown because a definite construction method for all BIBDs is still unknown. The study aimed to develop
a new construction method that could aid in constructing more BIBDs. The study derived a new class of
BIBD from un-reduced BIBD with parameters 𝑣 and 𝑘 such that 𝑘 β₯ 3 through selection of all blocks within
the un-reduced BIBD that contains a particular treatment 𝑖 then in the selected blocks treatment delete
treatment 𝑖 and retain all the other treatments. The resulting BIBD was Derived Reduced BIBD with parameters 𝑣
β = 𝑣 β 1, 𝑏
β = (
𝑣β1
𝑘β1
), 𝑘
β = 𝑘 β 1, 𝑟
β = (
𝑣β2
𝑘β2
), 𝜆 = (
𝑣β3
𝑘β3
) . In conclusion, the construction
method was simple and could be used to construct several BIBDs, which could assist in solving the problem
of BIBD, whose existence is still unknown