Best Known (85, 85+38, s)-Nets in Base 2
(85, 85+38, 72)-Net over F2 — Constructive and digital
Digital (85, 123, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 41, 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
(85, 85+38, 112)-Net over F2 — Digital
Digital (85, 123, 112)-net over F2, using
(85, 85+38, 677)-Net in Base 2 — Upper bound on s
There is no (85, 123, 678)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 10 874515 572375 775428 819221 270291 125612 > 2123 [i]