Best Known (1, 6, s)-Nets in Base 2
(1, 6, 5)-Net over F2 — Constructive and digital
Digital (1, 6, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- nets constructed from net-embeddable BCH codes [i]
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(1, 6, 5)-Net in Base 2 — Upper bound on s
There is no (1, 6, 6)-net in base 2, because
- 1 times m-reduction [i] would yield (1, 5, 6)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 34 > 25 [i]