Characterization of {2( q+1)+2,2; t, q}-minihypers in PG( t,q) ( t⩾3, qϵ{3,4})

Abstract

A set F of f points in a finite projective geometry PG( t, q) is an ( f, m; t, q};-minihyper if m (⩾0) is the largest integer such that all hyperplanes in PG( t,q) contain at least m points in F. Hamada and Deza (1988) characterized all {2( q+1)+2,2; t, q}-minihypers for t⩾3, q⩾5. Hamada (1987, 1989) also determined the cases of t=2, q⩾3. In this paper we characterize {2( q+1)+2,2; t, q}-minihypers for t⩾3, qϵ{3,4}. In addition to the previously known constructions, we describe a new {10, 2; 3,3}-minihyper.