Best Known (89, 129, s)-Nets in Base 2
(89, 129, 72)-Net over F2 — Constructive and digital
Digital (89, 129, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 43, 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
(89, 129, 116)-Net over F2 — Digital
Digital (89, 129, 116)-net over F2, using
(89, 129, 697)-Net in Base 2 — Upper bound on s
There is no (89, 129, 698)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 698 502114 269583 710617 796069 749706 697086 > 2129 [i]