Forty-three balanced incomplete block designs

AbstractThis paper gives 43 new BIBDs (balanced incomplete block designs); most of them have r ⩽ 41 and are thus additions to the list by Mathon and Rosa (Ars Combin. 30 (1990), 65–96). Some of these BIBDs are resolvable. Also included are (v, 7, 3) BIBDs for v = 519, 665 and some (p2 + 1, p(p2 + 1)2, p(p + 1)2, p + 1, (p + 1)2) BIBDs for p a prime power