Best Known (84, 84+42, s)-Nets in Base 2
(84, 84+42, 68)-Net over F2 — Constructive and digital
Digital (84, 126, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 63, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(84, 84+42, 96)-Net over F2 — Digital
Digital (84, 126, 96)-net over F2, using
(84, 84+42, 525)-Net in Base 2 — Upper bound on s
There is no (84, 126, 526)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 87 519382 513073 574211 867405 515551 827872 > 2126 [i]