How to calculate Best Linear Unbiased Estimator (BLUEs) from Fit Model in JMP

[#1]

I have an experiment with several different plant genotypes replicated across blocks. I fit a model where y = some plant trait and where the model effects are Block and Genotype. 

I want to calculate the BLUEs for the trait values of each genotype, giving an adjusted mean trait value for each genotype after accounting for the effect of Block. 

My intuition is that the BLUEs will be the Least Squares Means for Genotype in the model output. Is this correct, or are the BLUEs found somewhere else in the model output?

[#2]

See this help page for some related information.

[#3]

The help page refers to best linear unbiased predictors (BLUPs) of random effects. However, to be more clear, I want to treat Genotype as a fixed effect and find the best linear unbiased estimates (BLUEs rather than BLUPs).  I suspect that JMP calculates these but just does not name them as such.  For example, as I said above, I wonder if the BLUEs are equivalent to the LS Means for Genotype (fixed effect), or perhaps I use the prediction equation to calculate them?  

[#4 · Accepted solution]

The BLUEs are the parameter estimates. See this reference. The REML procedure that is used by default in the case of a random effect includes an adjustment of the degrees of freedom. The BLUEs are used to compute the LS Means for the categorical levels of genotype.