Best Known (17, 34, s)-Nets in Base 2
(17, 34, 18)-Net over F2 — Constructive and digital
Digital (17, 34, 18)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 9)-net over F2, using
- digital (5, 22, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
(17, 34, 44)-Net over F2 — Upper bound on s (digital)
There is no digital (17, 34, 45)-net over F2, because
- 1 times m-reduction [i] would yield digital (17, 33, 45)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(233, 45, F2, 16) (dual of [45, 12, 17]-code), but
- residual code [i] would yield linear OA(217, 28, F2, 8) (dual of [28, 11, 9]-code), but
- adding a parity check bit [i] would yield linear OA(218, 29, F2, 9) (dual of [29, 11, 10]-code), but
- residual code [i] would yield linear OA(217, 28, F2, 8) (dual of [28, 11, 9]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(233, 45, F2, 16) (dual of [45, 12, 17]-code), but
(17, 34, 53)-Net in Base 2 — Upper bound on s
There is no (17, 34, 54)-net in base 2, because
- 1 times m-reduction [i] would yield (17, 33, 54)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(233, 54, S2, 16), but
- the linear programming bound shows that M ≥ 26 525718 020096 / 2907 > 233 [i]
- extracting embedded orthogonal array [i] would yield OA(233, 54, S2, 16), but