X−1-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Some Balanced Bipartite Row-column Designs

A series of balanced bipartite row-column designs (BBPRC-designs) into sets of treatments with v1=4t+3 (test treatments) v2=2t+2 (control treatments) with varying replication has been obtained by supplementing a set of v2=2t+2 treatments in blank positions of non-orthogonal RC design of Agrawal (1966). Such designs find applications in agricultural and industrial experimentation where the inves...

On row-column directed block designs

Given a BIBD(v,k,A) we can construct a directed BIBD(v,k,A*) by writing each block of the BIBO twice, the second time in the reversed order. Here we prove the analagous expected but useful result that if a BIBD(v,b,r ks,k,A) exists, then a RCOBIBD(v,k,A *} also exists. A nonexistence result is also given.

Balanced Treatment-Control Row-Column Designs

Row-column designs (RCD) are used in experimental situations when the heterogeneity in the experimental material is due to two cross classified sources. In such trials, there may be situations in which the experimenter wants to compare a set of new (test) treatments with an already existing (control) treatment. The experimenter is interested in comparing test treatments with the control with mo...

A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties

Some Pairwise Balanced Designs

A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...