A method of constructing generalized difference sets

B. T. Rumov

Matematičeskie zametki, Tome 15 (1974) no. 4, pp. 551-560

Résumé

On the elements of the ring of residues modulo $v(2\nmid v,3\nmid v)$ we construct cyclic PBIB-designs with $\tau(v)-1$ classes of connectedness, where $\tau(v)$ is the number of divisors of $v$. We prove the existence of cyclic BIB-designs with parameters $b$, $v$, $r$, $k$ and $\lambda$ such that: 1) $\lambda=k$ (and also $\lambda=k/2$ if $k$ is even), $k\ge4$, and $k-1\mid p-1$ for each prime divisor $p$ of the number $v$; 2) $\lambda=(k-l)/2$, $k$ odd, $k\ge3$, $k\mid p-1$ for each prime divisor $p$ of the number $v$.