Best Known (18, 18+19, s)-Nets in Base 2
(18, 18+19, 17)-Net over F2 — Constructive and digital
Digital (18, 37, 17)-net over F2, using
- t-expansion [i] based on digital (15, 37, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(18, 18+19, 18)-Net over F2 — Digital
Digital (18, 37, 18)-net over F2, using
- net from sequence [i] based on digital (18, 17)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 18 and N(F) ≥ 18, using
(18, 18+19, 46)-Net over F2 — Upper bound on s (digital)
There is no digital (18, 37, 47)-net over F2, because
- 1 times m-reduction [i] would yield digital (18, 36, 47)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(236, 47, F2, 18) (dual of [47, 11, 19]-code), but
- adding a parity check bit [i] would yield linear OA(237, 48, F2, 19) (dual of [48, 11, 20]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(236, 47, F2, 18) (dual of [47, 11, 19]-code), but
(18, 18+19, 52)-Net in Base 2 — Upper bound on s
There is no (18, 37, 53)-net in base 2, because
- 1 times m-reduction [i] would yield (18, 36, 53)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(236, 53, S2, 18), but
- the linear programming bound shows that M ≥ 20 856361 189376 / 247 > 236 [i]
- extracting embedded orthogonal array [i] would yield OA(236, 53, S2, 18), but