Best Known (52, 85, s)-Nets in Base 2
(52, 85, 44)-Net over F2 — Constructive and digital
Digital (52, 85, 44)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 86, 44)-net over F2, using
- trace code for nets [i] based on digital (9, 43, 22)-net over F4, using
- net from sequence [i] based on digital (9, 21)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 9 and N(F) ≥ 22, using
- net from sequence [i] based on digital (9, 21)-sequence over F4, using
- trace code for nets [i] based on digital (9, 43, 22)-net over F4, using
(52, 85, 52)-Net over F2 — Digital
Digital (52, 85, 52)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 86, 52)-net over F2, using
- trace code for nets [i] based on digital (9, 43, 26)-net over F4, using
- net from sequence [i] based on digital (9, 25)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 9 and N(F) ≥ 26, using
- net from sequence [i] based on digital (9, 25)-sequence over F4, using
- trace code for nets [i] based on digital (9, 43, 26)-net over F4, using
(52, 85, 236)-Net in Base 2 — Upper bound on s
There is no (52, 85, 237)-net in base 2, because
- 1 times m-reduction [i] would yield (52, 84, 237)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 20 311099 992029 217159 750214 > 284 [i]