Best Known (156, 156+49, s)-Nets in Base 2
(156, 156+49, 195)-Net over F2 — Constructive and digital
Digital (156, 205, 195)-net over F2, using
- 8 times m-reduction [i] based on digital (156, 213, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 71, 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, 71, 65)-net over F8, using
(156, 156+49, 322)-Net over F2 — Digital
Digital (156, 205, 322)-net over F2, using
(156, 156+49, 3513)-Net in Base 2 — Upper bound on s
There is no (156, 205, 3514)-net in base 2, because
- 1 times m-reduction [i] would yield (156, 204, 3514)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 25 753303 400058 959078 674675 814247 695250 640302 306090 895485 699323 > 2204 [i]