All reports by Author Alex Vardy:

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TR17-070
| 15th April 2017
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Shachar Lovett, Sankeerth Rao Karingula, Alex Vardy#### Probabilistic Existence of Large Sets of Designs

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TR13-126
| 11th September 2013
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Arman Fazeli, Shachar Lovett, Alex Vardy#### Nontrivial t-designs over finite fields exist for all t

Shachar Lovett, Sankeerth Rao Karingula, Alex Vardy

A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been introduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain conditions, a randomly chosen structure has the required properties of a $t-(n,k,?)$ combinatorial design with tiny, yet ... more >>>

Arman Fazeli, Shachar Lovett, Alex Vardy

A $t$-$(n,k,\lambda)$ design over $\mathbb{F}_q$ is a collection of $k$-dimensional subspaces of $\mathbb{F}_q^n$, ($k$-subspaces, for short), called blocks, such that each $t$-dimensional subspace of $\mathbb{F}_q^n$ is contained in exactly $\lambda$ blocks. Such $t$-designs over $\mathbb{F}_q$ are the $q$-analogs of conventional combinatorial designs. Nontrivial $t$-$(n,k,\lambda)$ designs over $\mathbb{F}_q$ are currently known ... more >>>