[[Combinatorics MOC]]
# $t$-design

A $t-(n,k,\lambda)$ **design** $(S, \mathscr B)$ consists of a set $S$ of $n$ points
and a set $\mathscr B \sube \mathcal{P}(S)$ of distinguished subsets of $k$ points, called **blocks**, such that
for every $T \sube S$ with $\abs T = t$, there is exactly are exactly $\lambda$ blocks $B \in \mathscr{B}$ such that $T \sube B$.[^1999]

- A $t-(n,k,1)$ design is a $\opn S(t,k,n)$ [[Steiner system]]

  [^1999]: 1999\. [[Sources/@vanlintIntroductionCodingTheory1999|Introduction to coding theory]], §1.3, p. 17

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