But, of course, with no pair of treatments repeated together we cannot hope to be very close to that. This is
 a classical design of known high efficiency so that we should not be surprised that the range is very small.
 We can recognize also that for the design in blocks of four to be superior to the RCB in blocks of 16 the
 error variance for the blocks of four needs to be reduced by a factor of only

 (0.707/0.796)2 = 0.79

 which should be more than likely with a sensible choice of blocks.

 2.3 Only 15 varieties in Blocks of 3 and 4, or all 5

 Suppose the number of varieties had been 15. There are two interesting alternatives. One would be to use
 the design for example 2 simply omitting one of the treatments and using the resulting mixture of blocks of
 three and four plots. The other would be to use three blocks of five plots per replicate.

 For the first design we omit treatment 13 (arbitrarily) from the design, renumbering the subsequent
 treatments, and the resulting design is

 Replicate 1
 Block 1 Block 2 Block 3 Block 4
 (1,2,3,4) (5,6,7,8) (9,10,11,12) (14.15.16)

 Replicate 2
 Block 5 Block 6 Block 7 Block 8
 (1,5,9) (2,6,10,13) (3,7,11,14) (4.8,12,15)

 Replicate 3
 Block 9 Block 10 Block 11 Block 12
 (1,6,11,15) (2,5,12,14) (3,8,9,13) (4,7,10)

Replicate 4
 Block 13 Block 14 Block 15 Block 16
 (1,7,12,13) (2,8,11) (3,5,10,15) (4,6,9,14)

For the design in blocks of five plots, we start by using an arbitrary split into the three blocks.

Replicate 1
 Block 1 Block 2 Block 3
 (1,2,3,4,5) (6,7,8,9,10) (11,12,13,14,15)

Now each block in the second replicate must have one or two varieties from each of the first three blocks.

Replicate 2
 Block 4 Block 5 Block 6
 (1,6,7,11,12) (2,3,8,13,14) (4,5,9,10,15)