Best Known (18, 18+17, s)-Nets in Base 2
(18, 18+17, 19)-Net over F2 — Constructive and digital
Digital (18, 35, 19)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 9)-net over F2, using
- digital (6, 23, 10)-net over F2, using
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 6 and N(F) ≥ 10, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
(18, 18+17, 51)-Net over F2 — Upper bound on s (digital)
There is no digital (18, 35, 52)-net over F2, because
- 1 times m-reduction [i] would yield digital (18, 34, 52)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(234, 52, F2, 16) (dual of [52, 18, 17]-code), but
- residual code [i] would yield linear OA(218, 35, F2, 8) (dual of [35, 17, 9]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(234, 52, F2, 16) (dual of [52, 18, 17]-code), but
(18, 18+17, 60)-Net in Base 2 — Upper bound on s
There is no (18, 35, 61)-net in base 2, because
- 1 times m-reduction [i] would yield (18, 34, 61)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 17402 548237 > 234 [i]