Best Known (233−52, 233, s)-Nets in Base 2
(233−52, 233, 260)-Net over F2 — Constructive and digital
Digital (181, 233, 260)-net over F2, using
- 21 times duplication [i] based on digital (180, 232, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 58, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 58, 65)-net over F16, using
(233−52, 233, 430)-Net over F2 — Digital
Digital (181, 233, 430)-net over F2, using
(233−52, 233, 5221)-Net in Base 2 — Upper bound on s
There is no (181, 233, 5222)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 13829 551951 350508 587507 127077 590583 593769 783176 815855 940608 506961 844680 > 2233 [i]