TY - JFULL
AU - Oluwaseun. A. Alawode and Timothy. A. Bamiduro and Adekunle. A. Eludire
PY - 2012/9/
TI - Some (v + 1, b + r + λ + 1, r + λ + 1, k, λ + 1) Balanced Incomplete Block Designs (BIBDs) from Lotto Designs (LDs)
T2 - International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
SP - 1193
EP - 1197
EM - oa.alawode@mail.ui.edu.ng
VL - 6
SN - 1307-6892
UR - http://waset.org/publications/155
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 68, 2012
N2 - The paper considered the construction of BIBDs using potential Lotto Designs (LDs) earlier derived from qualifying parent BIBDs. The study utilized Li’s condition pr t−1 ( t−1 2 ) + pr− pr t−1 (t−1) 2 < ( p 2 ) λ, to determine the qualification of a parent BIBD (v, b, r, k, λ) as LD (n, k, p, t) constrained on v ≥ k, v ≥ p, t ≤ min{k, p} and then considered the case k = t since t is the smallest number of tickets that can guarantee a win in a lottery. The (15, 140, 28, 3, 4) and (7, 7, 3, 3, 1) BIBDs were selected as parent BIBDs to illustrate the procedure. These BIBDs yielded three potential LDs each. Each of the LDs was completely generated and their properties studied. The three LDs from the (15, 140, 28, 3, 4) produced (9, 84, 28, 3, 7), (10, 120, 36, 3, 8) and (11, 165, 45, 3, 9) BIBDs while those from the (7, 7, 3, 3, 1) produced the (5, 10, 6, 3, 3), (6, 20, 10, 3, 4) and (7, 35, 15, 3, 5) BIBDs. The produced BIBDs follow the generalization (v + 1, b + r + λ + 1, r +λ+1, k, λ+1) where (v, b, r, k, λ) are the parameters of the (9, 84, 28, 3, 7) and (5, 10, 6, 3, 3) BIBDs. All the BIBDs produced are unreduced designs.
ER -