The class of nearly balanced incomplete block designs with concurrence range l, or NBBD(l), is defined. This extends previous notions of “most balanced” designs to cover settings where off-diagonal entries of the concurrence matrix must differ by a positive integer l ≥ 2. Sufficient conditions are found for optimality of NBBD(2)’s under type-1 criteria, then used to establish Aand D-optimality ...

In a completely randomized design the experimental material is divided into a number of units, or plots, to which a treatment can be applied. In a randomized block design the units are grouped into blocks so that the variation within blocks is less than the variation between blocks. If every treatment is applied to one plot in each block it is a complete block design. If there are fewer plots p...