CHARACTERIZATION OF (2(Q-MINIHYPERS IN PG(T,Q) (T-GREATER-THAN-OR-EQUAL-TO-3, Q-IS-AN-ELEMENT-OF(3,4))(1)+2, 2 T, Q))

A set F off points in a finite projective geometry PG(t, q) is an (f m ; t, q}-minihyper if m (greater-than-or-equal-to 0) is the largest int eger 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 greater-than-or-equal-to 3, q greater-than-or-equal- to 5. Hamada (1987,1989) also determined the cases of t = 2, q greater -than-or-equal-to 3. In this paper we characterize {2(q + 1)+ 2, 2; t, q}-minihypers for t greater-than-or-equal-to 3, q is-an-element-of {3 , 4}. In addition to the previously known constructions, we describe a new {10, 2; 3, 3}-minihyper.