Hello,
I have a similar question. Recently we did NGS library preparation for target enrichment of genomic libraries and we used the NEBNext® Multiplex Oligos for Illumina with double indexing. I read somewhere that NEBnext kits are based on the TruSeq kits and therefore have the same adapters. So when i used fastqc to check the raw data i found some universal Illumina adapter. I trimmed those with the default TruSeq fasta in trimmomatic because i did not know that NEBnext might have additional adapters not recognized by fastqc. Can we say that all adapter sequences have been removed in this case? Can it be that fastqc does not recognize any additional adapter sequences of NEBnext kit and additional trimming is required? Is the core adapter sequence you are referring to the same as the universal illumina adapter i mentioned above? Any help would be appreciated.
It is not necessary to see adapter sequences in your data. If you have inserts that are smaller than number sequencing cycles then that is the only time one would read into adapter on 3'-end of fragment.