Best Known (57, 81, s)-Nets in Base 2
(57, 81, 72)-Net over F2 — Constructive and digital
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
(57, 81, 92)-Net over F2 — Digital
Digital (57, 81, 92)-net over F2, using
(57, 81, 552)-Net in Base 2 — Upper bound on s
There is no (57, 81, 553)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2 469201 357045 648102 933912 > 281 [i]