Best Known (188−47, 188, s)-Nets in Base 2
(188−47, 188, 195)-Net over F2 — Constructive and digital
Digital (141, 188, 195)-net over F2, using
- t-expansion [i] based on digital (140, 188, 195)-net over F2, using
- 1 times m-reduction [i] based on digital (140, 189, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 63, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- trace code for nets [i] based on digital (14, 63, 65)-net over F8, using
- 1 times m-reduction [i] based on digital (140, 189, 195)-net over F2, using
(188−47, 188, 266)-Net over F2 — Digital
Digital (141, 188, 266)-net over F2, using
(188−47, 188, 2608)-Net in Base 2 — Upper bound on s
There is no (141, 188, 2609)-net in base 2, because
- 1 times m-reduction [i] would yield (141, 187, 2609)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 197 238144 539530 451625 750416 272369 420839 744366 823440 736384 > 2187 [i]