Best Known (58, 82, s)-Nets in Base 2
(58, 82, 72)-Net over F2 — Constructive and digital
Digital (58, 82, 72)-net over F2, using
- 21 times duplication [i] based on digital (57, 81, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 27, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- trace code for nets [i] based on digital (3, 27, 24)-net over F8, using
(58, 82, 96)-Net over F2 — Digital
Digital (58, 82, 96)-net over F2, using
(58, 82, 585)-Net in Base 2 — Upper bound on s
There is no (58, 82, 586)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 4 851161 228558 600668 947872 > 282 [i]