Constructions for rotational near resolvable block designs (Q2725041)

The paper provides direct and recursive constructions for rotational near resolvable block (NRB) designs with particular attention to 1-rotational ones. In fact, the following material will be discussed: (1) rotational NRB designs associated with semiregular frames; (2) characterization of 1-rotational NRB designs in terms of differences; (3) construction for \(k\)-rotational \((kq+ 1,k,k-1)\)-NRB designs with \(q\) an odd prime power; (4) construction for 1-rotational \((pq+ 1,p,p-1)\)-NRB designs with \(p\) and \(q\) odd prime powers; (5) bound for a function \(g(q)\) defined in Definition 5.3; (6) comparison with the available Furino bound with some tables; (7) variant construction; (8) recursive construction; and (9) construction for 1-rotational \((5q+ 1,5,4)\)-NRB designs with \(q\) a prime power.