Suppose that we decided in the first replicate to put varieties 1 and 2 in block 1 and varieties 3 and 4 in
 block 2. In the second replicate varieties I and 3 in block 3, varieties 2 and 4 in block, and the other
 variety pairings in the third replicate, producing the following (rather like a split-plot design!)

 Block 1 (1,2,5,6,9,10) Block 2 (3,4,7,8,11,12)
 Block 3 (1,3,5,7,9,11) Block 4 (2,4,6,8,10,12)
 Block 5 (1,4,5,8,9,12) Block 6 (2,3,6,7,10,11)

 The range of standard errors for estimated treatment differences is

 0.82 a to 0.88 o with a mean of 0.87 a,

 fractionally better than the two earlier designs but for all practical purposes unchanged.

 Suppose we think in a "split-plot" pattern keeping similar date treatments together.

 Block 1 (1,2,3,4,5,6) Block 2 (7,8,9,10,11,12)
 Block 3 (1,2,3,4,11,12) Block 4 (5,6,7,8,9,10)
 Block 5 (1,2,9,10,11,12) Block 6 (3,4,5,6,7,8)

 The range of standard errors for estimated treatment differences is

 0.82 a to 0.93 a with a mean of 0.88 o.

 This time the precision is marginally worse than our first two designs but again the change is insignificant.

 Suppose we just try pretty patterns within the structured set of treatments.

 Block 1 (1,3,6,8,9,11) Block 2 (2,4,5,7,10,12)
 Block 3 (1,2,7,8,9,10) Block 4 (3,4,5,6,11,12)
 Block 5 (1,3,6,8,9,11) Block 6 (2,4,5,7,10,12)

 The range of standard errors for estimated treatment differences is

 0.82 a to 0.97 o with a mean of 0.90 a.

 A little bit worse both in mean S.E. and in the increased range but really the penalty for lack of thought,
 and even for repearing the division of replicate I in replicate 3 is very small.

 Finally we actually try to make the divisions into two blocks unnecessarily similar in the different
 replicates.

 Block 1 (1,2,6,7,11,12) Block 2 (3,4,5,8,9,10)
 Block 3 (1,3,5,8,9,11) Block 4 (2,4,6,7,10,12)
 Block 5 (1,4,5,8,9,10) Block 6 (2,3,6,7,11,12)

The range of standard errors for estimated treatment differences is

0.82 o to 1.10 a with a mean of 0.90 a.

Well, we have produced at least one rather poor precision comparison but the mean is still not much wo,-e
than our best efforts and even using the mean S.E. for the maximum S.E. would hardly be a disaster. A'
least for this design problem the moral is that if one makes any real attempt to produce a design according
to the defined principles it is actually rather difficult not to arrive at a good design.