Sandy Ferret

The Classification of the Largest Caps in AG(5, 3)

We prove that 45 is the size of the largest caps in AG(5,3), and such a 45-cap is always obtained from the 56-cap in PG(5,3) by deleting an 11-hyper-plane.

Results on Maximal Partial Spreads in PG (3, p 3 ) and on Related Minihypers

AbstractThis article classifies all {δ(q + 1), δ 3, q}-minihypers, δ small, q = ph0, h ≥ 1, for a prime number p0 ≥ 7, which arise from a maximal partial spread of deficiency δ. When q is a third power, the minihyper is the disjoint union of projected PG(5,

A classification result on weighted {δv µ+1 ,δv µ ;N,p 3 }-minihypers

\sqrt[3]{q}

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

)s; when q is a square, also Baer subgeometries PG(3,

A classification result on weighted {δv m N , p 3 }-minihypers

\sqrt q

A characterization of multiple (n – k)-blocking sets in projective spaces of square order

) can occur. This leads to a discrete spectrum for the small values of the deficiency δ of the corresponding maximal partial spreads.