Maximal partial spreads and the modular n-queen problem III

Abstract

Maximal partial spreads in PG(3,q) q=p k, p odd prime and q⩾7, are constructed for any integer n in the interval ( q 2+1)/2+6⩽ n⩽(5 q 2+4 q−1)/8 in the case q+1≡0,±2,±4,±6,±10,12 ( mod 24) . In all these cases, maximal partial spreads of the size ( q 2+1)/2+ n have also been constructed for some small values of the integer n. These values depend on q and are mainly n=3 and n=4. Combining these results with previous results of the author and with that of others we can conclude that there exist maximal partial spreads in PG(3,q), q=p k where p is an odd prime and q⩾7, of size n for any integer n in the interval ( q 2+1)/2+6⩽ n⩽ q 2− q+2.