Construction of Some Resolvable <i>t</i>-designs

Abstract

Abstract:The 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. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs. Additionally, an alternative approach for the construction of t-designs that provides a unified framework is also presented.

t-designs involving treatment combinations for animal experimentation

“…Chee et al (1990) presented a set of tables of t-designs of small order having no repeated blocks for treatment number less than 30. David (2017) constructed some resolvable t-designs by identifying BIB designs which are also t-designs. Trung (2017Trung ( , 2018 gave recursive methods of construction for simple t-designs satisfying a certain set of inequalities of the ingredient designs.…”