I wish to analyze the effect of tillage, nitrogen and cover crops on weed communities. The design can be described as the following: 

- 4 blocks

- main plot factor: tillage (nested in blocks)

- sub plot factor: nitrogen (nested in tillage) 

- sub sub plot factor: cover crops  (nested in nitrogen)

Hence, in a classical univariate mixed model (lme syntax), the error structure would be defined as (1|block/tillage/nitrogen) if only one sample is present at the sub sub plot level.

Now, I wish to analyse in R the effects of tillage*nitrogen*cover crops (all simple effects, all second order interactions and the third order interaction) on weed communities through partial CCA (to filter out the block effect).

I believe the following CCA model is correct (in {vegan}):

cca2013=cca(log(cover_2013+1)~tillage*N*CC+Condition(block),data=cover_2013)

And from what I gathered on the {permute} vignette,  the permutation design should be defined the following way:

h

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