Best Known (163−58, 163, s)-Nets in Base 2
(163−58, 163, 68)-Net over F2 — Constructive and digital
Digital (105, 163, 68)-net over F2, using
- 5 times m-reduction [i] based on digital (105, 168, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 84, 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
- trace code for nets [i] based on digital (21, 84, 34)-net over F4, using
(163−58, 163, 102)-Net over F2 — Digital
Digital (105, 163, 102)-net over F2, using
(163−58, 163, 532)-Net in Base 2 — Upper bound on s
There is no (105, 163, 533)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11 879414 024616 934330 225596 116994 190476 424099 012992 > 2163 [i]