Best Known (115, 163, s)-Nets in Base 2
(115, 163, 112)-Net over F2 — Constructive and digital
Digital (115, 163, 112)-net over F2, using
- 1 times m-reduction [i] based on digital (115, 164, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 82, 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, 82, 56)-net over F4, using
(115, 163, 157)-Net over F2 — Digital
Digital (115, 163, 157)-net over F2, using
(115, 163, 1051)-Net in Base 2 — Upper bound on s
There is no (115, 163, 1052)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11 929231 079955 336843 414237 495212 439305 263713 240493 > 2163 [i]