Happy Halloween!

I want to share some cool results of a project I’m working on in one of my classes. A *covering array* is a 4-tuple which is an array, each entry is from an alphabet of size , and for every of the columns, all -tuples over exists in at least one row when restricted to these columns. The *covering array number*, , is the smallest for which a exists. Kleitman and Spencer, and Katona independently, found for all ; no other cases are known for all , and only heuristics are known. My advisor keeps the best-known covering array numbers here.

I was able to show the following:

- ,
- ,
- ,
- ,
- ,
- .

The numbers in parentheses are the row reductions from previous known bounds. I won’t share how I did this yet, but it is a cool computational technique that works very well for high !

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