An algebraic study of BIB designs: A complete solution for v = 6 and k = 3

The set of all distinct blocks of a BIB design is referred to as the support of the design. The family of BIB designs with v = 6 and k = 3 is studied in depth from the view of possible support sizes. Via a linear algebraic technique it is shown that: (i) a BIB design with v = 6 and k = 3 exists if and only if the support size belongs to {10, 14, 16, 17, 18, 19, 20}; (ii) the minimum block size, b, needed to obtain a BIB design with support size $\text{b}{}^1$ is given by:

$\text{b}{}^1$	10	14	16	17	18	19	20
$\text{b}$	10	20	20	30	40	30	20
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