**Balanced incomplete block** is a reduced
version of the balanced complete block design. The design is incomplete if each of the *n* blocks tests only* c* of
the *a* levels of treatment A, where *c* < *a*. It is
balanced provided that each treatment level is tested the same number of times,
given by *r* = *nc*/*a*,
and each pair of treatment levels appears in the same number of blocks, given by
*λ* = *nc*(*c*-1)/[*a*(*a*-1)]. Likewise, a
two-factor blocked design is incomplete if *c* <* ab* combinations of
levels of the two treatments A and B, and it is balanced if integer values
pertain for both *r* = *nc*/(*ab*)
and
*λ* = *nc*(*c*-1)/[*ab*(*ab*-1)]. In the
example on these web pages, *a* = 4, *n* = 6, *c* = 2, so *
r* = 3 and *λ* = 1. The four levels of factor A could represent a
single treatment with four levels, or the four combinations of levels of two
treatments each with two levels.

Doncaster, C. P. & Davey, A. J. H. (2007) *Analysis of Variance and Covariance: How to
Choose and Construct Models for the Life Sciences*. Cambridge: Cambridge
University Press.

http://www.southampton.ac.uk/~cpd/anovas/datasets/