Best Known (172, 225, s)-Nets in Base 2
(172, 225, 195)-Net over F2 — Constructive and digital
Digital (172, 225, 195)-net over F2, using
- 12 times m-reduction [i] based on digital (172, 237, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 79, 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, 79, 65)-net over F8, using
(172, 225, 362)-Net over F2 — Digital
Digital (172, 225, 362)-net over F2, using
(172, 225, 4099)-Net in Base 2 — Upper bound on s
There is no (172, 225, 4100)-net in base 2, because
- 1 times m-reduction [i] would yield (172, 224, 4100)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 27 030450 327419 847342 169592 463107 057361 069984 368703 895983 395002 570240 > 2224 [i]