A classification result on weighted {δ ( p 3 + 1), δ; 3, p 3 }‐minihypers

We classify all {δ ( p 3  + 1), δ; 3, p 3 }‐minihypers, $\delta \leq 2p^2-4p, p=p_0^{h}\geq 9, h \geq 1$ , for a prime number p 0  ≥ 7, with excess e ≤  p 3 . Such a minihyper is a sum of lines and of possibly one projected subgeometry PG (5, p ), or a sum of lines and a minihyper which is a projected subgeometry PG (5, p ) minus one line. When p is a square, also (possibly projected) Baer subgeometries PG (3, p 3/2 ) can occur. © 2004 Wiley Periodicals, Inc.