engleski

A Construction of Some Symmetric (144, 66, 30) Designs

Let $q$ be a prime power, $q \equiv 1\ (mod\ 4)$, and let $p=\frac{; ; q-3}; ; {; ; 2}; ; $. We prove that there exists an orbit structure for the parameters $(4(p+1)^2, 2p^2 +3p+1, p^2 + p)$ and the orbit size distribution with $q+1$ fixed points and $2q$ orbits of size $p$ for points and blocks. Further, we describe a construction of four symmetric designs with parameters (144, 66, 30). These designs have the full automorphism group isomorphic to $(D_{; ; 10}; ; \times Frob_{; ; 13 \cdot 3}; ; ).Z_2$, and their 2-rang is 62.

symmetric design; Menon design; Hadamard matrix

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