Best Known (163, 163+84, s)-Nets in Base 2
(163, 163+84, 112)-Net over F2 — Constructive and digital
Digital (163, 247, 112)-net over F2, using
- 13 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 130, 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, 130, 56)-net over F4, using
(163, 163+84, 160)-Net over F2 — Digital
Digital (163, 247, 160)-net over F2, using
(163, 163+84, 912)-Net in Base 2 — Upper bound on s
There is no (163, 247, 913)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 232 612985 993530 782292 482314 495526 832837 708715 255738 286268 422404 687541 446272 > 2247 [i]