Best Known (89−46, 89, s)-Nets in Base 2
(89−46, 89, 33)-Net over F2 — Constructive and digital
Digital (43, 89, 33)-net over F2, using
- t-expansion [i] based on digital (39, 89, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(89−46, 89, 34)-Net over F2 — Digital
Digital (43, 89, 34)-net over F2, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 43 and N(F) ≥ 34, using
(89−46, 89, 95)-Net over F2 — Upper bound on s (digital)
There is no digital (43, 89, 96)-net over F2, because
- 2 times m-reduction [i] would yield digital (43, 87, 96)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(287, 96, F2, 44) (dual of [96, 9, 45]-code), but
(89−46, 89, 97)-Net in Base 2 — Upper bound on s
There is no (43, 89, 98)-net in base 2, because
- 2 times m-reduction [i] would yield (43, 87, 98)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(287, 98, S2, 44), but
- the linear programming bound shows that M ≥ 903696 228678 327600 676360 683520 / 4669 > 287 [i]
- extracting embedded orthogonal array [i] would yield OA(287, 98, S2, 44), but