Best Known (185−53, 185, s)-Nets in Base 2
(185−53, 185, 112)-Net over F2 — Constructive and digital
Digital (132, 185, 112)-net over F2, using
- 13 times m-reduction [i] based on digital (132, 198, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 99, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- trace code for nets [i] based on digital (33, 99, 56)-net over F4, using
(185−53, 185, 186)-Net over F2 — Digital
Digital (132, 185, 186)-net over F2, using
(185−53, 185, 1386)-Net in Base 2 — Upper bound on s
There is no (132, 185, 1387)-net in base 2, because
- 1 times m-reduction [i] would yield (132, 184, 1387)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 24 763838 159291 209026 731818 743197 588710 331088 997689 497726 > 2184 [i]