I am struggling with creating the appropriate model matrix for the type of comparisons I want to make. The data I have are from four different yeast strains, two conditions, and three replicates (total of 24 samples) (ex: Y184-YPD-rep1, Y184-NaCl-rep1, etc.). I want to make comparisons between the two conditions within a strain and make comparisons between the strains in each condition. I need to account for a strain-condition interaction as well as their additive effect in my model, so my first design was:

design.1<-model.matrix(~0 + strain*condition + rep)

but then the column names for this design are:

colnames(design.1)
 [1] "strainbcy1"                  "strainira2"                  "strainira2bcy1"              "strainY184"                
 [5] "conditionYPD"                "rep2"                        "rep3"                        "strainira2:conditionYPD"    
 [9] "strainira2bcy1:conditionYPD" "strainY184:conditionYPD"

which to me makes it seem like the NaCl condition isn't there, and I can't make a comparison with it?

So I've also tried this model, which accounts for only the interaction between strain and condition:

design.2<-model.matrix(~0 + strain:condition + rep)

and the column names makes it seem like everything is being accounted for

colnames(design.2)
 [1] "rep1"                         "rep2"                         "rep3"                        
 [4] "strainbcy1:conditionNaCl"     "strainira2:conditionNaCl"     "strainira2bcy1:conditionNaCl"
 [7] "strainY184:conditionNaCl"     "strainbcy1:conditionYPD"      "strainira2:conditionYPD"    
[10] "strainira2bcy1:conditionYPD"  "strainY184:conditionYPD"

But then moving on to modeling the dispersion with design.2, I get an error that I can't really figure out how to fix:

my.yglm.2<-estimateDisp(my.dge, design.2)
Error in glmFit.default(sely, design, offset = seloffset, dispersion = 0.05,  :
  Design matrix not of full rank.  The following coefficients not estimable:
 strainY184:conditionYPD

I've been messing around with a bunch other models, but nothing gives me the coefficient names I want in order to set the contrasts I want.

In another design, I use a grouping factor that combines the strain and condition into one (strain_condition -> listed like Y184_YPD) so I'm not considering the strain and condition separately, but I'm worried that it's not really accounting for the interaction I expect:

design.3<-model.matrix(~0 + strain_condition+rep)
colnames(design.3)
 [1] "strain_conditionbcy1_NaCl"     "strain_conditionbcy1_YPD"      "strain_conditionira2_NaCl"     "strain_conditionira2_YPD"      "strain_conditionira2bcy1_NaCl" "strain_conditionira2bcy1_YPD"
 [7] "strain_conditionY184_NaCl"     "strain_conditionY184_YPD"      "rep2"                          "rep3"

Any advice on where to go from here would be great!