According to my interpretation of Table I of http://neilsloane.com/doc/Me54.pdf it was not known at the time whether you needed bit ($q=2$) strings of length $n=22$, or possibly only of length $n=21$, to construct a set of $x=50$ codewords that are separated from each other by at least Hamming distance $d=10$. This particular example may or may not still be an open question, but there is probably not a known general formula for $n$ in terms of $q$, $x$, and $d$.
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