Getting a "system is computationally singular" error in sleuth
This happen when the variables (strain +batch) create a design matrix like this:

batch strain
1 1 #
1 1 #
1 2
2 2
3 3
4 3
...
16 72


Which means that some of the covariates are not linearly independent (ie batch 1 and strain 1), all the strain 1 is in batch 1. 

You can correct for batch effects, but not in this design of the linear model (if you want to take into account the strain). You could do one batch more with those 15 strains that are in a single batch (if they are in different batch between them) that way you would get an independent design.

Many strains in a single batch are in the same batch. You need to increase the number of samples (recommended anyway due to the low number of samples per strain) to avoid this problem. 



There are a lot of related question in Bioconductor support forum, from where I expanded an answer.