It looks like this is a MiSeq run as well, and by default De-multiplexing is part of the standard MiSeq workflow even if you don't send samples to MiSeq reporter for on-board analysis. In which case Nick you should inform them of this so they don't confuse other customers. Also, the lab in question really needs to do their homework a bit more before they start providing data to outside groups/labs...
I haven't done Illumina de-multiplxing before as the lab I am used to work with has done this by default. I'm now getting samples from a lab that says that it doesn't do de-multiplexing. It's a new lab which doesn't have experience with NGS so I am not quite sure they now what they are doing. So I got the following Illumina run (this is just a screenshot showing some of the files):

The SampleSheet in this folder has the following content (again a screenshot):

To me it looks like the data has been already de-multiplexed as the fastq files have the same names as the samples. What do you think? How can I test whether this is, indeed, the case? Also, I see some files (their names start with "Undetermined") which are not assigned to any sample. What shall I do with them?
1 answer
These are indeed demultiplexed. Providing demultiplexed files is such a simple thing for a sequencing facility to do that I'm always amazed when one is too lazy to do so. The "Undetermined" files can be ignored. I never provide those to our users. I should note, though, that I routinely check how many reads are in that file, simply because if those files are large then there was an issue with the library or sequencing.
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