Best Known (57−21, 57, s)-Nets in Base 2
(57−21, 57, 42)-Net over F2 — Constructive and digital
Digital (36, 57, 42)-net over F2, using
- 1 times m-reduction [i] based on digital (36, 58, 42)-net over F2, using
- trace code for nets [i] based on digital (7, 29, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- trace code for nets [i] based on digital (7, 29, 21)-net over F4, using
(57−21, 57, 43)-Net over F2 — Digital
Digital (36, 57, 43)-net over F2, using
(57−21, 57, 205)-Net in Base 2 — Upper bound on s
There is no (36, 57, 206)-net in base 2, because
- 1 times m-reduction [i] would yield (36, 56, 206)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 73480 005109 491318 > 256 [i]