My old job was basically the company BLAST-monkey, I could probably give you some specific help in a personal converstation.
However, I havent ran any BLAST searches in the last couple of years that I could share.
A couple of general points though:
- 99.9% (<-- pure guess based on extenisve observations!) of BLAST searches are run with whatever defaults are set by the web-portal or command line.
The speed of BLAST and related programs has been "fast enough" now for many years. So any improovments would need to come with "better" results (e.g. more accurate sequence alignments) to get the field excited.
The Hamming distance, is not really applicable in this field (although as an intermediate pass the pre-filter a database of sequences it may have some use), as e-values are the cut-off most frequently used. However this depends largely on the reason of the search, and if you are looking for evolutionary related protein sequences or short stretches of highly similar DNA. For the latter, take a look at BLAT (https://genome.ucsc.edu/FAQ/FAQblat.html) which last time I checked was orders of magnitude faster than BLAST at these type of searches.
If you want me to cobble together a test datbase or two with some general & more tricky edge examples I could do.
This is not a Signature...