Coset-k 2 Nested Balanced Incomplete Block Designs of Resolvable Type

Saka, J, Adeleke B, Jaiyeola T.  2018.  Coset-k 2 Nested Balanced Incomplete Block Designs of Resolvable Type, 2018/10/01. 8:267-273.


This paper presents, a new method of constructing nested balanced incomplete block designs (NBIBDs) of resolvable type called Coset-k 2 , using an algebraic notion, of the left coset type. The class of NBIBDs that was constructed for ′í µí±£′ treatments arranged in 'b' blocks of size ′í µí±˜′ each with í µí±£ = í µí±˜ 2 and other parameters of the design are expressed as (í µí±˜ 2 , í µí±˜ + 1, í µí±˜ + 1, í µí±˜(í µí±˜ + 1), í µí±˜ 2 , í µí±˜, í µí±˜ + 1, í µí±˜ 0 , í µí±˜). Indeed, the parameters of the design for any given number of treatments, v, are specified with ease even before the full designs are constructed. Also, fewer numbers of blocks are required when compared with the designs of comparable sizes. Designs that are constructed in this paper are appropriate for experiments where extraneous factors of two types if they exist can be eliminated, evaluated and controlled.