Best Known (129, 129+54, s)-Nets in Base 2
(129, 129+54, 112)-Net over F2 — Constructive and digital
Digital (129, 183, 112)-net over F2, using
- 9 times m-reduction [i] based on digital (129, 192, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 96, 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, 96, 56)-net over F4, using
(129, 129+54, 173)-Net over F2 — Digital
Digital (129, 183, 173)-net over F2, using
(129, 129+54, 1159)-Net in Base 2 — Upper bound on s
There is no (129, 183, 1160)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12 446819 500038 581526 495279 058025 405396 287664 590050 506288 > 2183 [i]