Super-simple balanced incomplete block designs with block size 5 and index 3

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple (v,5,3) balanced incomplete block design and show that such a design exists if and only if v=1,5(mod20) and v>=21 except possibly when v=45,65.

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