A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3...) occurs. The problem of finding all parameters (t, v, k, λ_t) for which t-(v, k, λ_t) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. The objective of this study therefore to develop new methods of constructing t-designs with t ≥ 3 and λ ≥1. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs.
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