Not Availablealpha-designs are essentially resolvable block designs. In a resolvable block design, the blocks can be
grouped such that in each group, every treatment appears exactly once. Resolvable block designs allow
performing an experiment one replication at a time. For example, field trials with large number of crop
varieties cannot always be laid out in a single location or a single season. Therefore, it is desired that
variation due to location or time periods may also be controlled along with controlling within location or
time period variation. This can be handled by using resolvable block designs. Here, locations or time
periods may be taken as replications and the variation within a location or a time period can be taken care
of by blocking. In an agricultural experiment, for example, the land may be divided into a number of large
areas corresponding to the replications and then each area is subdivided into blocks. These designs are
also quite useful for varietal trials conducted in the NARS and will help in improving the precision of
treatment comparisons. A critical look at the experimentation in the NARS reveals that alpha designs
have not found much favour from the experimenters. It may possibly be due to the fact that the
experimenters may find it difficult to lay their hands on these alpha-designs. The construction of these
designs is not easy. An experimenter has to get associated with a statistician to get a randomized layout
of this design. For the benefit of the experimenters, a comprehensive catalogue of alpha-designs for
6 <=v(= sk) <= 150, 2 <= r <= 5, 3 <= k <= 10 and 2 <= s <= 15 has been prepared along with lower bounds
to A- and D- efficiencies and generating arrays.
The layout of these designs along with block contents has also been prepared. The designs obtained have
been compared with corresponding Square Lattice, Rectangular Lattice, Resolvable two-associate
Partially Balanced Incomplete Block (PBIB (2)) designs and the alpha-designs obtainable from basic arrays
given by Patterson et al. (1978). Eleven designs are more efficient than the corresponding resolvable
PBIB (2) designs (S11, S38, S69, S114, LS8, LS30, LS54, LS76, LS89, LS126 and LS140). It is
interesting to note here that for the PBIB (2) designs based on Latin square association scheme, the
concurrences of the treatments were 0 or 2 and for singular group divisible designs the concurrences are
either 1 or 5. Further all the designs LS8, LS30, LS54, LS76, LS89, LS126 and LS140 were obtained by
taking two copies of a design with 2-replications. 10 designs were found to be more efficient than the
designs obtainable from basic arrays. 48 designs (29 with k = 4 and 19 with k = 3) are more efficient than
the designs obtainable by dualization of basic arrays. 25 designs have been obtained for which no
corresponding resolvable solution of PBIB(2) designs is available in literature. The list of corresponding
resolvable PBIB(2) designs is S28, S86, SR18, SR41, SR52, SR58, SR66, SR75, SR80, R42, R70, R97,
R109, R139, T14, T16, T20, T44, T48, T49, T72, T73, T86, T87 and M16. Here X# denotes the design of
type X at serial number # in Clatworthy(1973).Not Availabl
