Best Known (94−51, 94, s)-Nets in Base 2
(94−51, 94, 33)-Net over F2 — Constructive and digital
Digital (43, 94, 33)-net over F2, using
- t-expansion [i] based on digital (39, 94, 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
(94−51, 94, 34)-Net over F2 — Digital
Digital (43, 94, 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
(94−51, 94, 95)-Net over F2 — Upper bound on s (digital)
There is no digital (43, 94, 96)-net over F2, because
- 7 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
(94−51, 94, 96)-Net in Base 2 — Upper bound on s
There is no (43, 94, 97)-net in base 2, because
- 3 times m-reduction [i] would yield (43, 91, 97)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(291, 97, S2, 48), but
- adding a parity check bit [i] would yield OA(292, 98, S2, 49), but
- the (dual) Plotkin bound shows that M ≥ 158456 325028 528675 187087 900672 / 25 > 292 [i]
- adding a parity check bit [i] would yield OA(292, 98, S2, 49), but
- extracting embedded orthogonal array [i] would yield OA(291, 97, S2, 48), but