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Stefan Kohl ♦
Stefan Kohl ♦
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A $(n,n/2,\lambda)$ block-design is a family $A_1,...,A_K$ of subsets of $[n]$ such that $|A_i|=n/2$ and for every $1 \leq i < j \leq n$ it holds that: $\#\{1 \leq k \leq K : i,j \in A_k \} = \lambda$. My question is: What is the minimal $K$ for which such a design exists?

A $(n,n/2,\lambda)$ block-design is a family $A_1,...,A_K$ of subsets of $[n]$ such that $|A_i|=n/2$ and for every $1 \leq i < j \leq n$ it holds that: $\#\{1 \leq k \leq K : i,j \in A_k \} = \lambda$. My question is: What is the minimal $K$ for which such a design exists?

A $(n,n/2,\lambda)$ block-design is a family $A_1,...,A_K$ of subsets of $[n]$ such that $|A_i|=n/2$ and for every $1 \leq i < j \leq n$ it holds that $\#\{1 \leq k \leq K : i,j \in A_k \} = \lambda$. My question is: What is the minimal $K$ for which such a design exists?

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Lior
Lior
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Minimal number of blocks in a $(n,n/2,\lambda)$ block design

A $(n,n/2,\lambda)$ block-design is a family $A_1,...,A_K$ of subsets of $[n]$ such that $|A_i|=n/2$ and for every $1 \leq i < j \leq n$ it holds that: $\#\{1 \leq k \leq K : i,j \in A_k \} = \lambda$. My question is: What is the minimal $K$ for which such a design exists?