Best Known (82, 82+36, s)-Nets in Base 2
(82, 82+36, 72)-Net over F2 — Constructive and digital
Digital (82, 118, 72)-net over F2, using
- 21 times duplication [i] based on digital (81, 117, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 39, 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, 39, 24)-net over F8, using
(82, 82+36, 112)-Net over F2 — Digital
Digital (82, 118, 112)-net over F2, using
(82, 82+36, 684)-Net in Base 2 — Upper bound on s
There is no (82, 118, 685)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 337265 829022 453602 646695 812710 198460 > 2118 [i]