Best Known (163, 163+74, s)-Nets in Base 2
(163, 163+74, 112)-Net over F2 — Constructive and digital
Digital (163, 237, 112)-net over F2, using
- 23 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+74, 188)-Net over F2 — Digital
Digital (163, 237, 188)-net over F2, using
(163, 163+74, 1188)-Net in Base 2 — Upper bound on s
There is no (163, 237, 1189)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 226750 760714 600821 267945 780409 493641 429053 524509 253153 346467 944653 378018 > 2237 [i]