Multiple coverings of the farthest-off points ((R,µ)-MCF codes) and the corresponding (�,µ)-saturating sets in projective spaces PG(N,q) are considered. We propose and develop some methods which allow us to obtain new small (1,µ)-saturating sets and short (2,µ)-MCF codes with µ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1 + 1/cq, c ≥ 1). In particular, we provide new algebraic constructions and some bounds. Also, we classify minimal and optimal (1,µ)-saturating sets in PG(2,q), q small.
['Daniele Bartoli', 'Alexander A. Davydov', 'Massimo Giulietti', 'Stefano Marcugini', 'Fernanda Pambianco']
Further results on multiple coverings of the farthest-off points