A classification result on weighted {δvμ+1,δvμ;N,p3}{δvμ+1,δvμ;N,p3}-minihypers

We classify all {δvμ+1,δvμ;N,p3}{δvμ+1,δvμ;N,p3}-minihypers, δ⩽2p2-4pδ⩽2p2-4p, p=p0h⩾11, h⩾1h⩾1, for a prime number p0⩾7p0⩾7, with excess e⩽p3-4pe⩽p3-4p when μ=1μ=1 and with excess e⩽p2+pe⩽p2+p when μ>1μ>1. For N⩾4N⩾4, p   non-square, such a minihyper is a sum of μμ-dimensional spaces PG(μ,p3)PG(μ,p3) and of at most one (possibly projected) subgeometry PG(3μ+2,p)PG(3μ+2,p); except for one special case when μ=1μ=1. When p   is a square, also (possibly projected) Baer subgeometries PG(2μ+1,p3/2)PG(2μ+1,p3/2) can occur.