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A series of Menon designs and 1-rotational designs

Let $p$ and $2p+3$ be prime powers and $p \equiv 3\ (mod\ 4)$. We describe a construction of a symmetric design D with parameters $(4(p+1)^2, 2p^2 +3p+1, p^2 + p)$. If $p$ and $2p+3$ are primes, then a derived design of D is 1-rotational.

Menon design; Regular Hadamard matrix; Symmetric design; 1-Rotational design

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