Rule for blocks with replicates for default designs
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For a blocked default design with replicates, Minitab puts replicates in different blocks to the extent that it can.

The following rule is used to assign runs to blocks: Let k = the number of factors, b = the number of blocks, r = the number of replicates, and n = the number of runs (corner points).

Let D = the greatest common divisor of b and r. Then b = B*D and r = R*D, for some B and R. Start with the standard design for k factors, n runs, and B blocks. (If there is no such design, you will get an error message.) Replicate this entire design r times. This gives a total of B*r blocks, numbered 1, 2, ... , B, 1, 2, ...  , B, ... , 1, 2, ... , B. Renumber these blocks as 1, 2, ... , b, 1, 2, ... , b, ... , 1, 2, ... , b. This will give b blocks, each replicated R times, which is what you want.

For example, suppose you have a factorial design with 3 factors and 8 runs, run in 6 blocks, and you want to add 15 replicates.

Then k = 3, b = 6, r = 15, and n = 8. The greatest common divisor of b and r is 3. Then B = 2 and R = 5. Start with the design for 3 factors, 8 runs, and 2 blocks. Replicate this design 15 times. This gives a total of 2*15 = 30 blocks, numbered 1, 2, 1, 2, 1, 2, ... , 1, 2. Renumber these blocks as 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, ... , 1, 2, 3, 4, 5, 6. This gives 6 blocks, each replicated 5 times.