The Spectrum of Support Sizes of $BIB$ Designs with $v=10$ and $k=5$

Abstract

The support of a $t$-design is the set of all distinct blocks of the design. The support size of a design is denoted by $b^{\ast }$. In this paper, except for $b^{\ast }=23$, we completely determine the spectrum of support sizes of the case $v=10$, $k=5$, and $t=2$.