Designs over finite fields
Let F be a finite field. A t-(n,k,\(\lambda)\)-design over F is a collection of k-dimensional subspaces (``blocks'') of \(F^ n\) with the property that every t-space is contained in exactly \(\lambda\) blocks. This generalizes the notion of an ordinary t-design. Prior to the paper under review, no non-trivial examples are known for \(t\geq 2\). (Spreads yield examples for \(t=1.)\) The author constructs a 2-(n,3,7)-design over GF(2) whenever \(\gcd (n,6)=1\). For \(n\geq 7\), these are non-trivial.
scientific article; zbMATH DE number 4019873