Best Known (122, 122+48, s)-Nets in Base 2
(122, 122+48, 112)-Net over F2 — Constructive and digital
Digital (122, 170, 112)-net over F2, using
- 8 times m-reduction [i] based on digital (122, 178, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 89, 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, 89, 56)-net over F4, using
(122, 122+48, 180)-Net over F2 — Digital
Digital (122, 170, 180)-net over F2, using
(122, 122+48, 1294)-Net in Base 2 — Upper bound on s
There is no (122, 170, 1295)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1514 645403 667712 588565 918502 226661 534630 260561 657392 > 2170 [i]